The topic of camera movement and lighting is too vast to fit in this thread. I suggest you read some tutorials online or buy some good cinematography books if your just looking for general tips.
DVD + Pause, examine every single shot and cut to see what they're doing (write them out - content, frame size, duration, movement, etc). Replicate/Rip Off their techniques / setups / pacing.
I too noticed, that there are many harsh shadows. Wally Pfister lights scenes very interestingly. In loads of scenes, i found that he light 2 shots, in the same scene and location very differently.
For example, when Bruce Wayne says goodbye to Alfred: Alfred has the windows behind him and has burned out highlights on the right/top righ of his face. When cut to Bruce however, who is standing quite close to him, but facing the windows, he has a very dark left side of the face. I found this quite interesting in the film and wondered what the reason for this was. Normally, Bruce's face should be a lot brighter. Maybe there is something blocking the light which wasn't seen in the film.
Like Paul said, even Batman's action sequences aren't like you find them in most films. The are mostly very smooth, shot on Crane's, Helicopters, Dollies and stuff like that. There's a good BTS on Youtube where you can see some of the shots with BTS! http://www.youtube.com/watch?v=61ta8lhLX60
I actually think that Batman's camera movements are too smooth and too subtle, but that's just me. Not that I really like Sam Raimi's opposite type of style either, but somewhere in between. But yeah just pay attention. Nolan uses a lot of slow tracks on dollies. Whether it is around the actors, or moving forward on them. Of course there are several other types he does as well. Just watch close.