Visible crew/equipment: After Batman and Robin use their infrared eyeglasses on the Parker boys, Batman turns on the emergency generator switch and Legs escapes. Then the Dynamic Duo deliver a bit of exposition, and when they walk over to Ma Parker, their curved chalk marks are visible on the floor behind Robin. (00:22:10)
Continuity mistake: When Batman is strapped into the electric chair, his utility belt is the standard flat-front, blank, yellow boxes. Once Batman breaks the wire loose to send a message, there is a large, black and yellow button attached to the the right front of the belt.
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