The Heist Itself (spoilers)
This falls easily under the category of "Because it's a movie, and if they didn't do it, there wouldn't be a plot." So we can get that out of the way up front.
But if we ignore that for a minute and move into the film's own internal logic and look for things that strain internal consistency, the thing that bothered me the most was the complexity of the heist.
There is a scene that focuses and highlights for the audience DeNiro's refusal to ever take a long shot or a caper that does not have a high probability of success. He spends quite a while telling Norton's character about his careful, cautious, and risk-averse strategy to jobs. Earlier dialog is also careful to stress the fact that DeNiro gets to set up every aspect of this operation and that the mechanics of the caper are entirely his.
Then when we watch the actual robbery in progress, it is impossibly complex, with unlimited chances for it to be shot to hell at every step.
1) The security codes are bought from rank amateurs who see key players in the robbery gang up close and personal. At any point those guys could have the codes changed, break under pressure, or just decide to rat out the team with an anonymous tip. They already have their money.
2) Split second timing relies on Norton's janitor character being alone, out of sight, and uninterrupted for a half hour during normal work hours. Yes, it's supposed to be during his "lunch" break, but as we see, that's a lot to rely on and can easily be messed up.
3) They know they are pulling down the security cameras in the most secure area of the building, monitoring a highly guarded, high-profile item that has received a ton of attention. And yet they are gambling that once the cameras die, no security guard will bother going down to check on it for fifteen uninterrupted minutes while DeNiro bores, fills, and blows the safe. A crazy assumption.
4) The amount of heavy, specialized gear that DeNiro has to carry, set up, perform acrobatics with, and operate perfectly is overwhelming. Each piece of the process adds another chance for something to go wrong. The cumulative probability of failure should be too high for DeNiro's comfort level.
5) The final double double-cross relies on an incredible assumption that if Norton crosses him, DeNiro will simply be able to swap out a lead pipe, secure in the knowledge that Norton won't check it. Other threads have pointed out that maybe we in the audience can strain credulity enough to think that Norton might not have checked in the stress of the moment... But I can't believe that DeNiro came up with a preset plan that RELIED on that oversight.
Oh well... That's the movie. Without it we are left with nothing. I just wish they hadn't given us so much setup beforehand on how risk-averse DeNiro is. His actions sure don't match up with his big talk.