Continuity mistake: After Annie drops the chandelier on them, Batman and Robin are knocked unconscious. No one's had time to move either of them, but when Andy comes into the saloon in the next shot, Robin has somehow shifted positions on the floor: he's not in the same spot or position he originally fell in. (00:21:30)
Continuity mistake: When Okie Annie shoots the chandelier over Batman and Robin, they both are dazed by it. But Shame only whacks Batman over the head with the chair before he falls unconscious. Robin is still waving his hands reacting to the chandelier fall and finally falls unconscious when Batman goes to the ground.
Revealing mistake: After Shame and his baddies steal Bruce's limo. Bruce shows Dick and Alfred that he had the remote control unit keep the Bat-cycle (with Alf-cycle) following them at a safe distance. In the shots facing the Bat-cycle, attached to the front wheel there's a rope pulling it. (00:17:05)
Other mistake: At the end of the episode when the cattle are stampeding, the sign over the Saloon is backwards.
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