I personally am an economic conservative, so while I will try to be unbiased please note that I may consciously or subconsciously be biased one way or the other.

There are two main economic critiques of the Great Depression. I say main because I am sure that there will be Marxists and Austrians flooding in (well, maybe not) to chip in their theories. But the two main theories are that of John Meynard Keynes, or the "Keynesian" school, and that of Milton Friedman, or the "Monetarist" school.

Both schools generally accept that the initial stock market crash was something that would happen. It was something with a very low chance of occurring, but by no means something that shouldn't have happened at all.

However, where they disagree is on what the proper response should have been by the government.

In the case of Keynes, the argument is essentially that around this time, aggregate demand, or basically how much people and companies wanted things, was low. In other words, people weren't spending money. The general economic theory was that people spend money to buy goods, which causes companies to expand production (in anticipation of future sales), which increases employment (and, after the population is almost entirely employed, wages), which in turn increases the amount of money people have, which in turns causes them to spend more. As a result, Keynes advocated that in this scenario, the government should have stepped in and provided employment, "digging holes and then filling them back in" if necessary. The idea was that the government, by providing workers with jobs, gives them money to spend, thus increasing investment and thus increasing employment. This is what we typically call fiscal policy.

On the other hand, the Monetarists led by Friedman argued that the Great Depression was caused by flawed monetary policy, or control over the supply of money. His argument was that because the Federal Reserve failed to support failing banks, people lost their savings, or those that did save their savings would hide it under their beds instead of storing it in a bank. As a result, banks could not lend money (as people didn't have any to save, or were scared that their bank would collapse also), which prevented companies from investing in the aforementioned cycle above, which would thus stall employment opportunities. The Monetarists thus argue that this failure to do so caused the recession to drag on for longer than necessary (hence, "depression"), because there was no capital for companies to borrow from at low enough rates.

To be perfectly frank, the Keynesians and the Monetarists agree on like 95% of most economic issues. In fact, Churchill used to refer to economics as "any two economists will give you two opinions, except if one of them is John Meynard Keynes, in which case you will have three opinions."

I think it is quite fair to say that in the economics literature, Friedman is largely considered to be right in this regard.

Friedman's core claim in his 1963 Monetary History of the United States is that the Federal Reserve made the Depression worse than it otherwise would have been via contractionary monetary policy in 1929-30. The Fed failed to be expansionary enough to offset the fall in aggregate demand in 1929-1933; as a result, nominal incomes fell in half, prices fell by a third and real output fell by about 25%. The early literature is summarized in this 1976 Meltzer article.

The Friedman-Schwartz hypothesis is largely taken as correct by Bernanke (1983 AER), which documents the role of financial factors in prolonging the Depression from 1930-1933. Note that he explicitly states in the opening paragraphs that he is not attempting to explain the decline in output from 1929-1930, seeing as it had been adequately solved by Friedman-Schwartz. Financial factors largely work to explain the prolonged nature of the Depression, but do not account for the drop in output from 1929-1930.

Barry Eichengreen, Jeffrey Sachs, and Peter Temin have focused on the role of the gold standard in inhibiting recovery from the Depression; see this representative 1985 JEH article. Again, they take the Friedman-Schwartz view of the Great Contraction for granted; footnote 1. Exchange-rate factors and nations' ties to the gold standard largely account for the speed or sluggishness of their recoveries, but not for the collapse in 1929-33 itself.

Christina Romer's influential 1992 JEH article focuses on the sources of recovery from 1935-1945, largely taking the Friedman-Schwartz view of the events of 1929-1933 for granted.

The role of tariffs is considered in Crucini and Kahn (1996 JME); their results are usefully summarized in this 2003 followup piece. In brief, tariff wars mattered but were small relative to everything else that was going on.

A useful 1997 review article is available here, which also takes Friedman and Schwartz seriously.

A recent paper is Eggertsson (2008 AER), which again focuses on the recovery but takes Friedman and Schwartz in stride.

You may also be interested in the 1993 symposium on the Depression held by the Journal of Economic Perspectives.

That gets at your money-and-the-Depression question. I'll have to reserve broader comments on Friedman and Capitalism and Freedom for another post.

I am largely citing from the scholarly economics and economic history literatures here; mods please let me know if that's a problem.