Revealing mistake: As the Batmobile exits the Batcave, if you watch the exit closely, you see the shadow of the back end of the car come to a stop, meaning that it was at the wall of the set. (00:05:10)
Revealing mistake: Riddler laughing maniacally after handing Batman the lawsuit turns around and leaves, not before tipping a vase over. There is a crashing noise as if the vase shattered, but the vase is tumbling in a full 360°, undamaged. (00:11:50)
Answer: There wasn't one singular city used. It was shot in and around various locations in California, plus on a lot of sets and backlots. Ex. Some scenes were shot in LA, some in Pasadena, some in Santa Barbara, etc.
TedStixon