1. Parliamentary systems have enabled a relatively peaceful transition from Monarchy and other autocratic forms of government to liberal democracy. There have been numerous parliamentary systems that have slowly devolved power from a monarch which has absolute power through councils and slowly into popular houses. The British Westminster is probably the best known of this form, though other nations have achieved similar devolutions. The complicated executive in the parliamentary system is a function of the original Executives - the Crown - slowly being shunted out of real political and executive power. While the Crown still has a real role in Britain, in Australia and Canada the Crown is written out of real political power by the Constitutions that place Crown power in a Governor-General or Viceroy as the Monarch's representative. It is accepted in modern parliamentary systems that the Ceremonial Executive will not act constitutionally unless on the advice of the Prime Minister.
2. Parliamentary systems allow for flexible legislative structures such as bicameral, unicameral, etc. Though this isn't unique to the Westminster system as the Washington style states in the United States have a mix of bicameral and unicameral legislatures as well. The Norwegian system included the lower house dividing itself after an election into an upper 'Lagting' and lower house though this was discontinued in 2009.
3. The Prime Minister, or head of the executive cabinet, can be replaced without an election. Poor performing or unpopular Prime Ministers can be replaced by the majority party without requiring the approval of the electorate. This is a function of the Executive not being directly elected as it is in a Presidential System such as the American Washington system. The American President can be removed via impeachment proceedings, but not because the majority party in Congress decides they need a new party leader. In a Parliamentary system the Prime Minister is the leader of the party able to form government and he can be removed as the leader of the majority party - and hence Prime Minister - independent of the electorate. This transition can be clean or it can be bumpy and antagonistic. The recent replacement of Kevin Rudd by Julia Gillard in Australia is a good recent example of the latter. The counter argument to a party removing a Prime Minister is that this is not what the electorate voted for, however, this is a difficult argument to make as voters do not vote directly for a Prime Minister in a parliamentary system.
4. A government can be removed from power through a no-confidence vote, causing new elections to be called. This is more a loss of confidence by the parliament in the executive than by the population at large but it ends in an orderly transition of power through the ballot box if voters decide to agree with the Parliament in the no confidence vote. The no confidence vote is by convention in Australia and Canada but is constitutionally entrenched in Germany.
5. The ceremonial executive has some reserve powers in most Westminster systems to provide a check and balance on the Executive Cabinet. This is doubtful if this is a good thing, and the constitutional crisis in Australia known as 'the dismissal' was divisive. There have only been two incidents of this nature in Australia, once at the national level, and once in NSW. A good example of these reserve powers being used in a positive manner was in Queensland when Joh Bjelke-Peterson wanted to dissolve his cabinet as his power was waning within the party, the Governor refused.
6. Allows for the Executive to move their policy agenda through the Legislative because the Executive is created from a majority in the Legislative's lower house. Because the Executive Cabinet and legislative majority are and the same, the executive cabinet is quickly able to move its agenda through the legislative process and begin executing those policies. There are less veto points for the Executive in a parliamentary system than there are in the Washington system.
7. Parliamentary systems have adopted varied, progressive and innovative electoral systems, possibly to compensate for the lack of separation of powers between the Executive and Legislative. The Japanese Diet uses a mix of first past the post and party list proportional system. Tasmania includes electoral innovations such as the Robson Rotation. This isn't unique to Parliamentary systems, as Chile's Presidential system supports a binomial election process in the lower house, but it is important that the parliamentary system can support electoral and democratic innovations.
8. Parliamentary systems have proved resilient when faced with minority government. The Australian national government recently became a minority government with Julia Gillard as Prime Minister. This has been rare at the national level in Australia, but common at the state level. Other nations with parliamentary systems and multiple parties have been dealing with minority governments for a while as well.
9. Parliamentary systems have been able to function without a formal constitution. Westminster systems are largely ones that have grown through evolution and convention. Many Westminster governments have no constitution to speak of. For instance Western Australia and South Australia have initial bills from the United Kingdom establishing them as self governing but no constitution describing how that government or system will function. It is purely based on convention. Other Australian states such as Queensland and New South Wales have a statutorial constitution where the functions of government are in one bill. Queensland recently modernised their constitution to put it in one statute. New South Wales has parts of its statutorial constitution requiring restrictions on its change such as majorities or referendums. Australia has a constitution like the United States Washington system.
10. Powers are constantly being devolved from the Ceremonial Executive and into more democratic bodies. For instance the Swedish Parliament recently changed from the King of Sweden asking the leader of the majority party or coalition to form government to the Speaker of the Riksdag.
11. Parliamentary systems have been able to support Federal structures. Federalism is a system where constituent political bodies have a parent governing body. Historically, Federalism has been a convenient way for small political bodies to nationalize. For instance in United States, Australia, Canada and India where colonies bonded to form a national body. In India the Rajya Sabha (upper house) is indirectly elected by the different states electing representatives to the national upper house. This isn't unique to the Westminster system as the Washington and Canton systems are also able to support Federalism.
1. Poor separation of powers. The executive is mixed with the Legislative. This has allowed bad legislation to pass through and then be executed in a heavy handed and arbitrary approach. The parliamentary system has limited checks and balances on the Executive especially. In unicameral structures that lack an upper house this is particularly bad. Institutions such as committee and inquiries have evolved to try and cover this problem but often the inquiries are limited by what the majority party will allow them to inquire into protecting the executive and committees in upper houses often contain members of the Executive Cabinet making checks and balances difficult. This poor separation of powers is the biggest problem of a parliamentary system.
2. Poor checks and balances from the Legislative on the Executive. In a Presidential system the Executive and Legislative are two separate bodies. The Legislative is the main body for creating policy whereas the Executive is the main body for implementing that policy. There is some overlap, for instance, executive orders can dictate in what manner a policy or statute will be implemented or executed. By the same token the Legislative can place in the statue limitations on how the policy will be executed. For the most part the Washington system requires a collegial relationship between the Executive and Legislative.
3. In bicameral systems the Cabinet is often chosen from the Senate or Upper House as well. This pollutes the intent of an upper house performing as a check and balance on the Lower House in the Legislative. One of the intents of an upper house is to act as a Legislative check and balance on the lower house. This check and balance can be watered down when the reach of the executive is in the upper house as well. Absolute party discipline over-rides this concern though as the party of the executive in the upper house has limited independence in this case.
4. Not immune to governance by executive exception, if anything it makes it easier because the executive is embedded in the legislative and controls the legislative agenda. One of the modern methods of governance is for the legislative to drop their role and place the running of government, in part, or in times in full, to the executive when there is a state of emergency. These can be real or imagined.
5. Informal constitutions that are either based on convention, multiple statues, or a single statue. The constitution itself is not entrenched and can be changed at any time by the Executive/Legislative via a bill or amendment. Numerous national governments, such as the United Kingdom, do not have a formal constitution and instead the practices of democracy are spread across numerous bills over history. It has been a pattern for modern parliamentary systems to modernise their constitutions - such as Canada and Queensland in Australia - to collapse all these informal and historical bills into one formal constitution. One of the aspects of an informal constitution that is statute based is one of the innovations of the Washington System - formally entrenched and explicit rights - are difficult to implement in the informal constitutional systems as they can be easily changed by statute and consequently are not entrenched or immutable rights. This is probably one of the largest differentiators between the Washington and Westminster systems.
6. Convention dominates practice. Because of the informal constitutional nature Westminster systems tend to run on convention. One of the downsides of convention is that it is great until someone breaks the convention and after that there is basically no going back to the old conventional ways. This is seen consistently in Australian politics. For instance it was the convention that the civil service would not be politicized, which remained the convention until it was no longer the convention, now the civil service and military are becoming increasingly politicized due to choices, decisions, policies and wishes of the executive. Another example of the breaking of convention leading to unintended consequences was prior to the Whitlam Dismissal when the states did not follow the convention of appointing Senators from the same party as the ones resigning and the Senate broke the convention of not blocking supply. Arguably there was precedent of a Governor-General dismissing a government prior to 1975 as Lang's NSW Government was dismissed by Governor Game in 1932.
7. Reserve Powers are inherently undemocratic and have been used in ways in the past that have caused constitutional crisis. In Australia the Governor-General is the crown's representative as the crown is the ultimate executive authority in the Australian Constitution. The Governor-General - and hence the crown as a constitutional monarch - acts on the advice of the Prime Minister, however the Australian Constitution allows for reserve powers as they are called. These are non specific powers where the Governor-General can dissolve a government. This is the basis of the Whitlam Dismissal in 1975. The Australian constitution is odd in this regard as it has a race condition where the Governor-General can sack a Prime Minister but a Prime Minister can sack a Governor-General.
8. Reserve Powers are often based on convention and uncertainty arises when they are used. The three main events in Australia where the reserve powers have been used were in the Whitlam Dismissal, the Lang Government sacking and the refusal of Governor Campbell in Queensland to sack Joh Bjelke-Petersons cabinet on Bjelke-Peterson's request. The dismissal in 1975 did cause confusion but fortunately there was a double dissolution election soon after which mirrored Kerr's decision. Secondly, the party being kicked out of government accepted it. Given the turmoil in 1932 where NSW came close to Civil War prior to the sacking of Lang, there was concern for social stability in 1975 when the politicians involved tried to work out what was going on and what to do from this use of reserve powers by Kerr.
9. Parliamentary systems tend to develop absolute political authority from the executive and are less collegial than the Congress in the United States. As a consequence party discipline becomes absolute in the house and often upper houses and there is less conscience voting in parliamentary systems. This is possibly more a result of the structure of modern political parties in the Westminster systems, particularly Australia's labor, but conscience voting in Australia only occurs in the majority party holding power when the Executive allows it.
10. The absolute authority of the Executive over the Legislative has led to a more and more autocratic form of party political power stemming from the Prime Minister. One of the modern maladies of modern liberal democracy is the state of exception where the executive acts independently of legislative approval and outside of judicial oversight. The parliamentary system is particularly vulnerable to this as there is no separation of powers in the lower house between the executive and the legislative. The Washington system has stronger separation of powers and the legislative sometimes claws back its legislative role to make policy for the executive to implement but it has been disappointing in this regard as well.
11. The Prime Minister is not elected directly and has little direct democratic legitimacy. In contrast the President in the Washington system is directly elected by the population. The Prime Minister is the leader of the political party that has a majority in the Lower House of the Legislative and is only directly elected to be a representative by one district. This is an issue for voters in parliamentary districts as they don't necessarily vote for who is best for their district, instead voting along presidential party lines. There is a certain union in this though, since the Prime Minister's party controls the legislative, there is a high probability that districts of the same party as the executive will get better funding.
12. Strategic voting for a Prime Minister that might not represent the electorates interests. A good representative for an electorate may be voted against in order to strategically vote for a majority party in order for a certain Prime Minister to be indirectly chosen.
13. Modern media, and modern political parties in the Parliamentary systems are running the position of Prime Minister like a directly elected Presidential one. This exacerbates the indirect voting for the executive problem.
14. Upper Houses tend to be non-democratic. This is more a historical hang-over of the way Westminster has been evolutionary, but it is a trait of the Westminster system that the Upper House in many countries is either hereditary or appointed by the Ceremonial Executive. Canada's Senate is appointed by the Viceroy on the advice of the Prime Minister. The Senators are tenured in the Senate until the age of 75. A position in The House of Lords in Britain is obtained by inheritance, appointment or because they are a Bishop. Recent reform in Britain has cut off the hereditary process for the House of Lords.
15. They are a hack to get around the Monarchy. The British parliament is a historical process of devolving power from an absolute monarch. This is the main reason for the confusing integration of executive powers in the crown, regents and executive in the house of representatives. Rather than a clean removal of the monarch as an executive as America's Washington system was able to do, the parliamentary and Westminster system have been a messy devolution of crown power into the hands of an elected majority. This is probably a good thing for those that believe in the ceremonial or cultural power of the monarch, for republicans the inherent in equality of a hereditary monarch is not something that should be sustained or supported constitutionally or politically.
16. Shared Executive powers to keep a ceremonial Executive in place. Australia has multiple 'top' executive positions, the Queen, the Governor-General who is the head of the Executive Council and the Prime Minister who is head of the Executive Cabinet. This is why the race condition between the Governor-General being able to sack the Prime Minister and the Prime Minister being able to replace the Governor-General exists. It all works well as long as people are reasonable and don't try to take the system to its natural or explicit ends in terms of challenging power amongst all the executive roles. The problem is that it only takes one unreasonable person to collapse these conventions and make them unworkable.
17. Powers are constantly being devolved from the Executive, for instance in Sweden the Crown no longer asks for a party to form government. While the crown exists as a political or constitutional entity, and since they have no democratic legitimacy any remaining powers the crown has will be devolved into more democratic bodies. However, in a system of separation of powers there are necessary roles for an executive and muddying of executive roles in a parliamentary system may mean the executive will lose those responsibilities and they will end up in the judicial or legislative.
18. Parliamentary Committees are used to keep a check on the Executive due to poor separation of powers. Since the Executive is in the legislative, the executive is often able to set the limits of what a committee can review and hence keep the public eye away from any executive wrong doing. This has become a standard political tactic in Australia.