The three things Moore is usually taken to task for are:

1) the Charlton Heston speech, which edited together phrases from several different speeches.

2) the claim that the Columbine students went bowling with their classmates the morning of the shooting. This is genuinely in dispute, with several eyewitnesses swearing they were there and several swearing they were not.

3) the scene in the bank where Moore gets a gun as a premium. According to the bank, normally you would have to go to a gun shop to get the gun, but Moore's producer had called ahead and asked them to have a gun in the bank. Moore says that this is a lie, and that they in fact had a whole vault full of guns. Either might be lying, but no one disputes that he showed what "really happened" that day in the bank, without "fictionalizing" anything. In any case, the surprising thing is that you can easily get a gun as a bank premium, not that the gun is physically in the bank!

I'm willing to concede that Moore's tricks, especially the one he played on Heston, may have stretched the boundaries of truth. But the only reason people are yelling about revoking the Oscar is because they don't agree with his politics. If "Winged Migration" had won, would people be complaining that "the birds wouldn't have acted that way if your plane hadn't been there?" How about "juxtaposing this shot of the flock of ducks with that one was fictionalizing the film because they were really filmed miles apart and on different days?" I think not. People normally don't care about this kind of thing, but when there's a political message they react according to their political position. Indeed, if Moore's editing had made Heston look more sensitive rather than less, the very people who are complaining would be happy as clams. So it's not about truth, it's about politics.

In the end, documentary filmmaking doesn't tell an unramified truth, and people who claim it does or think it should probably don't watch too many documentaries and therefore shouldn't be taken seriously when they say they know better than the academy.