The Clock King's Crazy Crimes (1) - S2-E11
Other mistake: When Clock King activates the coils to ensnare Batman and Robin, the coils ensnare Batman first, while Robin just reacts. In the next shot, Robin is tangled as well.
Other mistake: When Tut's henchman slowly reads that Bruce Wayne will donate his talking sphinx to the Black Museum at Scotland Yard from a newspaper, a close-up shows he is reading it upside down.
Hizzonner the Penguin (1) - S2-E17
Other mistake: When Pengy shows up at the Grand Order of Occidental Nighthawks he feigns shock, then as he shoves his umbrella into the vat of sulfuric acid, Penguin moves his arm/hand toward the right to pull out a different umbrella, one that appears destroyed by the acid. (00:22:55)
Other mistake: At the end of the episode when the cattle are stampeding, the sign over the Saloon is backwards.
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.
Dizzonner the Penguin (2) - S2-E18
Other mistake: In the fight in Convention Hall, when the goons surround Batman, watch the one on the front left. He's punching over and down, yet he's hitting nothing.
Dizzonner the Penguin (2) - S2-E18
Other mistake: Batman throws himself into acid. Counting on acid-proof suits, Batman comes out unscathed, but his ropes didn't get burned off until he dipped the back into the acid. Also, even though he covered his face a moment, he came out with his face exposed, and undamaged, when it should have been burned.
The Duo Is Slumming (2) - S2-E32
Other mistake: While Batman and Robin are ascending in the balloon, Robin picks up a chewed piece of gum, and stops the altimeter just before 20,000 feet. After that, Robin wondered how to get down. Beside Batman's head is the handle of the cord that would have started to let the air out, and started dropping them down.
Other mistake: The opening scene and dialogue with Bruce and Dick responding to Gordon's call is from The Curse of Tut.
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