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.
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