Revealing mistake: In the recap, in the wide shot where Mr Freeze uses his freeze gun on Batman and Robin, you can see they are stunt doubles.
Visible crew/equipment: When the photographer is getting a picture of the princess, you can see the shadow of the boom mic on him.
Other mistake: During the final fight scene between the SOCK and POW, Mr. Freeze can be seen in the 76-degree heated section.
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