Batman's Satisfaction (2) - S2-E52
Continuity mistake: While the Batcomputer starts acting wonky just as Batman and Robin need it to figure out Pinky's location, when Alfred joins Batman and Robin in the Batcave, the Yellow Pages phone book vanishes from the Batcomputer's shelf in the closeup. (00:12:20)
Caught in the Spider's Den (2) - S2-E56
Visible crew/equipment: In Commissioner Gordon's office, when Gordon and Chief O'Harah walk over to the Batphone so they can talk to Robin and get him to surrender, we can see the actor's white tape mark taped to the rug, just as Gordon removes the clear acrylic dome from the Batphone. (00:17:20)
Caught in the Spider's Den (2) - S2-E56
Audio problem: The sound effects are inaudible when Robin is punching Black Widow's henchman when she talks about where her short-circuiting device is.
Caught in the Spider's Den (2) - S2-E56
Visible crew/equipment: When Batman and Robin are caught in Black Widow's web, the wires used to operate the spiders are visible.
Pop Goes the Joker (1) - S2-E57
Continuity mistake: After Oliver Muzzy congratulates Joker for his magnificent artwork and makes a deal with him, before Joker leaves the gallery he runs his finger across Batman's yellow emblem to sign his red artwork, but at GCPD HQ when they're discussing the matter, Joker's signature is completely different, it's now a capital "J" on Batman's yellow emblem. (00:06:45)
Pop Goes the Joker (1) - S2-E57
Other mistake: Not only can Caesar Romero's moustache can be seen, but the line between the white makeup and his skin on his neck. Also, when Robin's face came out of the clay, his mask was almost around his mouth. A moment later, the mask is back in place. Later, his face, mask, and body is spotless.
Flop Goes the Joker (2) - S2-E58
Revealing mistake: At the "Batfight", the Joker leaves the room and he kidnaps Baby Jane but when it cuts back to the fight, if you look closely at the door, the Joker can be seen leaving the room again. Note his iconic pink suit.
Flop Goes the Joker (2) - S2-E58
Revealing mistake: After Bruce stops the governor of the mobile, it can be seen that the weights are painted Styrofoam balls.
Visible crew/equipment: After the first couple of shots of the Batcopter, when it cuts to Mr. Freeze at his refrigerated refuge, the two black tape marks are visible on the floor near Professor Isaacson's and Glacia's feet.
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