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.
Batman Displays His Knowledge (2) - S2-E50
Continuity mistake: When Batman and Robin are trying to escape from the giant coffee cup at the beginning of this episode, spots of moisture keep appearing and disappearing on Batman's costume.
The Contaminated Cowl (1) - S2-E35
Continuity mistake: After the Mad Hatter's spray turns Batman's cowl pink, Batman and Robin are shown in the Batmobile, headed back to the Batcave. The stock shot shows Batman wearing his regular blue cowl while inside the car. Once they get to the Batcave, Batman's cowl is pink again.
Continuity mistake: When Batman is strapped into the electric chair, his utility belt is the standard flat-front, blank, yellow boxes. Once Batman breaks the wire loose to send a message, there is a large, black and yellow button attached to the the right front of the belt.
Other mistake: The opening scene and dialogue with Bruce and Dick responding to Gordon's call is from The Curse of Tut.
The Minstrel's Shakedown (1) - S2-E5
Plot hole: When Batman and Robin explain to the board members at the stock exchange that Minstrel will not be a threat because they dealt with Penguin, Archer, Clock King, King Tut, and Catwoman, in broadcast order, there is a 6-episode difference between Minstrel and Clock King who has never been seen before. To the first-time viewer, they were probably wondering who Clock King is.
Shoot a Crooked Arrow (1) - S2-E1
Continuity mistake: When Batman and Robin are ensnared by Archer's net, Batman says he will get his batknife to free them. When Archer shoots them down with the arrow, they are apparently unconscious but with no explanation of what knocked them out while stuck in the net.
Catwoman Goes to College (1) - S2-E49
Continuity mistake: When they first go to the bat poles, Bruce is on the right. The next shot at the bottom, Bruce/Batman is on the left and Dick/Robin is on the left. They switched sides. It has happened throughout the series.
The Sandman Cometh (1) - S2-E33
Continuity mistake: When Dick and Bruce go "to the bat poles" Dick is on the left side and Bruce on the right. When they get to the bottom, they have switched poles. Dick is on the right and Bruce is on the left.
The Joker's Provokers (2) - S2-E22
Factual error: During the fight to regain his box, the Joker picks up an orange colored deep well drill bit to hit Batman. First, such a device has sufficient weight that one regular man couldn't lift it easily, let alone swing it. Second, the drill bit wouldn't be lying around in the water works guard office.
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