The major problem I had was that the lawyer who found the plans for the Tumbler seemed to know that Bruce Wayne was Batman, which is essentially confirmed by Lucius Fox. All he knows is that Wayne Enterprise provides Batman with his technology.
Actually I think it would be far more likely that Batman is a average/non rich and famous citizen, but is just funded by someone rich, like Wayne.
As I've stated before I dislike the Tumbler and the motorcycle. I'm really hoping he gets a new Batmobile in the next film and it's not another Tumbler.
I was also hoping that Harley Quinn would be in the movie, I was pretty disappointed the Joker didn't have her helping him.
His stupid voice change when he is Batman.
I like his Batman voice, it really adds to his Batman persona. The only problem I had with it were that a couple of lines that are sort of hard to understand. One example is early in the movie when a fake Batman asks him what is the difference between them and he says "I don't wear a hockey mask" (which was a bad line in the first place, it should of been something like "I don't use guns" or "I don't kill people"). However I had no problems understanding 99% of his lines.