Smack in the Middle (2) - S1-E2
Deliberate mistake: Ignoring that its very unlikely all of Jill St. John's copious red hair would fit under a wig that passes for Robin's hair, it's impossible that it would emerge from under that wig looking as full and perfectly styled as it does when she's in the Batcave.
Smack in the Middle (2) - S1-E2
Continuity mistake: When Fake Robin takes Riddler's wheel to drive, the shot cuts to the Batmobile. It appears that Robin is a passenger, but he is supposed to be Riddler's prison service.
Smack in the Middle (2) - S1-E2
Revealing mistake: After Batman tosses his Batarang up to get to Molly, the lifting wire attached to him is plainly visible.
Smack in the Middle (2) - S1-E2
Factual error: Nitrous oxide is not flammable. Not to mention, if it were, Riddler would have risked blowing everything up when he shot the gun in the room saturated with it just to give his henchmen the signal.
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