Fine Feathered Finks (1) - S1-E3
Revealing mistake: At the start, Penguin's henchmen give out booby trapped umbrellas to everyone outside the House of Ali Baba. When they all enter the jewelry store those umbrellas explode with fireworks, gas, confetti, etc, and the stunt wires holding up the umbrellas are visible, at the top of the screen. (00:01:20)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: After the huge rooftop umbrella is launched onto the street there's a small umbrella hanging from its handle, and when Batman uses his Batarang to swing towards the huge umbrella's shaft, his stunt wires are visible. (00:18:45)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: When Penguin pulls the lever, Adam West assumes the position to receive the net dropped on his head a couple of seconds early and as if Bruce/Batman knew beforehand that something was coming from the ceiling, in that spot, passively accepting it. (00:22:10)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: In the close-ups of the basket filled with umbrellas at the bank, the asbestos blanket is continuously bumping up and shaken not by the 'explosions' of the booby trapped parasols, but rather by the thin wires you can make out at the top of the frame. (00:15:10)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: The trademark vertical rope climb of this episode is done on the handle of a huge umbrella. The umbrella though is at an angle in the various wide shots, and Batman is climbing a perfectly vertical handle. (00:18:30)
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