Continuity mistake: There is a jump cut at the beginning when Batman and Robin are being lowered into the vat of wax, where all of a sudden, Batman is trying to wiggle his legs free.
Continuity mistake: At the beginning, in the wide shot of Batman and Robin over the candle dipper, Riddler is standing with his back towards them, but in the close-up, he is facing forward.
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