The problem -- and you're right to bring this up -- is often that the "anti-Keynesians" and other non-readers constantly try to reduce Keynes only to the discussion of boosting aggregate demand.  Had this been his only point, The General Theory would've been no more than fifty pages long, instead of the roughly 400 pages he actually wrote.  Remember that the book is built, first and foremost (and contrary to what the title suggests), as a roadmap to ending the Great Depression, though it is applicable to recessions in general.

Keynes said many times that demand could easily be too high, causing inflation.  It just wasn't the case at the time he was writing his magnum opus.  Demand had collapsed.  And he knew that lowering interest rates more would do absolutely nothing, except cause more money to be stashed in coffee tins under citizens' beds.

You have to look at both sides.  People get caught up in what Keynes was saying about aggregate demand, but he was only saying it because a boost to aggregate demand was what the economy needed, desperately, at the time.  If you ever get a chance to read A Tract on Monetary Reform or The Economic Consequences of the Peace, I highly recommend both, because they'll give you a much better picture of how Keynes thought about inflation and deflation.  (As I recall, he even discusses asset bubbles, though that's not what he calls them.)

They're also much easier reads than The General Theory, which can seem like torture at times, because Keynes was explaining everything in such detail.

Another myth is that people will tell you Keynes believed recessions were caused by a fall in demand.  That may be true, but it's not what I got from him.  My interpretation is like Krugman's.  Keynes didn't give a damn about what caused a recession.  Recessions were, and are, a fact of life, even in non-capitalist countries, so asking what caused them was the wrong question.  He cared about how to combat them.

I think he probably would've advocated a greater emphasis on fiscal policy in the aftermath of the 2001 recession, especially once housing prices began taking off.  But, more than anything, I think the key understandings to take from him are those on inflation and deflation, and especially the fact that they do not produce simply the reverse effects of each other.

A critical point that I think you're getting at is that he's not the end-all, be-all of economics, but rather an important turning point -- away from myths like the idea that money is neutral; that prices and wages adjust instantly; and (most importantly) the idea of the "moral economy" (read: Austrian) where recessions are the result of past excesses and, therefore, cannot be fought.  There is a great deal more to work out, but questions, like those surrounding (say) asset bubbles, are small, relative to those he was working with.

Be nice to America. Or we'll bring democracy to your country.