Remember guys, TDK will not be in complete chronological order. Nolan said so, I believe it was at the WW panel.
It could be that the bank robbery happens late in the story, hence why the Joker has turned on the mob and hates Batman.
Yes, so the scene that begins the film is not where the story actually begins. Good point, well done. So, let's say the mob 'hires' Joker to go after Batman, but then they lose focus and interest in Joker. Maybe they even screw him over. Joker robs the bank to become the center of attention again, maybe get some revenge on the mob. (Bet his gang doesn't know his real motivation!) That all hangs together nicely as far as I am concerned, and is consistent with the confirmed details (the sides, the teaser) that we have.
This out-of-order theory also explains why the Joker is wearing a mask. By this point, his face is probably well-known, and he's something of a target. The bank manager, therefore, recognizes him, as the 'sides' dialogue implies. He says 'WHAT are you?' not 'WHO are you?', and he knows that Joker has a 'different' agenda ("Criminals in this town used to believe in things. Honor. Respect."). He's not saying this because Joker robs his bank, which he believes to be suicidal (he says as much before the mask comes off). He says this because he knows about other things Joker has done, and they make no sense to him.
Like the bank manager, WE also recognize Joker when we see him. So by presenting the bank scene out of order at the beginning, Nolan starts the film off by giving the audience a dramatic 'reveal' of the character. (Remember how Batman 89 handled this reveal, with Joker stepping out of the shadows?) No wonder he thought this scene was important enough to shoot with IMAX.
Normally, a thief burning money stolen from a bank would not actually wipe out that money. That money is insured by the Federal Government. Maybe since it is 'grey market' money it isn't properly insured, however. I suppose they can work around that point. Anyway, as others have said, the scheme does sound quite Jokerish. He's not motivated by money per se, and isn't THAT what Alfred was really saying in that teaser dialogue?