The Unkindest Tut of All - S3-E6
Continuity mistake: When the Batmobile pulls up to the theater where Tut's henchmen are emerging, Batman challenges them while standing at the open driver's side door. You can see his left hand closing the door, as well as hear it click shut - but in the next, reverse angle shot, as he and Robin leap into the fray, the car door is standing wide open again. (00:08:00)
The Unkindest Tut of All - S3-E6
Deliberate mistake: When Batman has figured out King Tut's plot to steal ancient Egyptian scrolls from the Gotham City Library, he and Robin rush away, and in the shot of the library exterior, the words "The New York Public Library" is quite noticeable above the entryway. (00:18:00)
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