Smack in the Middle (2) - S1-E2
Revealing mistake: When Batman bursts out from the mammoth, one of the 'unconscious' extras changes position reacting to the practical effect. (00:20:45)
Revealing mistake: As the Batmobile exits the Batcave, if you watch the exit closely, you see the shadow of the back end of the car come to a stop, meaning that it was at the wall of the set. (00:05:10)
The Pharaoh's in a Rut (2) - S1-E28
Revealing mistake: When Bruce Wayne is strapped to the stretcher hurtling toward the cliff, after he breaks through the "300 Ft. Drop" sign, we cut to a different angle where the wire pulling the stretcher is visible. (00:02:40)
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.
Enter Batgirl, Exit Penguin - S3-E1
Revealing mistake: The panel that Batgirl makes her entrance through can be plainly seen as a prop mounted on top of the set of stairs she comes down.
Surf's Up! Joker's Under! - S3-E10
Revealing mistake: When the Dynamic Duo are locked in the board blanks, you see the jets where the smoke and flame come out.
A Riddling Controversy (2) - S2-E46
Revealing mistake: When Batman and Robin use their jets to get out of the quicksand, as they fly up, you can see the wires used to pull them up.
The Joker's Provokers (2) - S2-E22
Revealing mistake: When Alfred talks to his twin Egbert, as they face each other, you can plainly see the line dividing the screen so that Alan Napier can play both parts.
An Egg Grows in Gotham (1) - S2-E13
Revealing mistake: A lot of the time, especially in close ups, you can see the line between the bald dome wig and Vincent Price's real skin, as well as the different coloring of skin.
The Bookworm Turns (1) - S1-E29
Revealing mistake: At about the 6:40 mark into the episode, The Bookworm puts an explosive device in the Batmobile which is detected automatically. Batman pushes the auto eject to throw it out of the car. As the special effects prop explodes, you can see the rope it is hanging from as it swings to the side.
Penguin's Clean Sweep - S3-E20
Revealing mistake: In any of the close up shots of Penguin, his nose has a completely different skin colour than the rest of his face. Making it very obvious that the actor is wearing a fake nose.
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