Dizzonner the Penguin (2) - S2-E18
Continuity mistake: In the beginning, Batman and Robin's side of the scales are lowering them down. At one point, it isn't moving.
Continuity mistake: Mr. Freeze has frozen the commissioner's office, and when Batman applies plastic explosive to the door, a frost stripe appears that wasn't there in the master shot a moment before. In the next shot, the putty he's just put there disappears. And when the explosion occurs (even though Batman didn't add any detonators), it doesn't emanate from anywhere near the spot where he applied the putty. (00:06:00)
The Impractical Joker (1) - S2-E21
Continuity mistake: Toward the end of the fight in the fur salon, one of Joker's henchmen shifts locations instantaneously. In the first shot, he's on the far side of Robin, falling against the wall. In the very next shot, he jumps to a spot between Robin and the camera, where he takes a swing at Batman. (00:17:00)
The Joker's Provokers (2) - S2-E22
Continuity mistake: While Joker and his baddies are in the vent shaft at the waterworks, Joker takes out the envelope and holds the envelope with his left palm up, but in the closeup his left palm is down as he pours the pills into his right hand. (00:14:50)
The Joker's Provokers (2) - S2-E22
Continuity mistake: After Alfred pulls out the key, two pieces of the little blue time-shifting box have apparently fallen to the floor. Joker snatches one of them up while struggling with the butler. But when Batman and Robin leap in for the next shot, the second piece has vanished from its spot on the floor. (00:20:30)
Marsha, Queen of Diamonds (1) - S2-E23
Continuity mistake: After Batman has been hit by Marsha's love dart, when Robin pulls the dart out and then begs Batman to resist it, in these semi closeups note Burt Ward's uncovered forearm with his still-healing burn wound. Then, while the Dynamic Duo fight Marsha's sabre wielding goons, Marsha hits Robin with another one of her darts and orders him to attack Batman. When this happens, Burt Ward's forearm now has a compression bandage around the wound. (00:13:55)
Marsha's Scheme of Diamonds (2) - S2-E24
Continuity mistake: In part 1, Marsha's prisoners included the mayor. Here, Batman rescues Robin, Gordon and O'Hara - but the mayor has disappeared. And oddly, no one mentions his ever having been there. (00:05:05)
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.
The Bird's Last Jest (2) - S2-E28
Continuity mistake: When the Dynamic Duo goes up the Bat Pole chute, the NEGATE COSTUME CHANGE lever is down. When they come down as Dick and Bruce, the lever is up, and Robin pulls it down to stop the instant change back to Dick and Bruce.
Continuity mistake: During the fight, the desk mat and desk calendar are moved initially and then moved again later in the fight. (00:19:03 - 00:22:00)
The Bat's Kow Tow (2) - S2-E30
Continuity mistake: When Catwoman tries to tempt Batman into a kiss at the end, his cape is draped completely over the right half of his chest. Each time the angle reverses, though, it's pulled back over his shoulder in its usual position. (00:21:15)
The Puzzles Are Coming (1) - S2-E31
Continuity mistake: In the Batcave, Batman is holding Puzzler's pink balloon while he and Robin deduce its clues. The shot cuts to a wider angle when they turn to race to the Batmobile, and the balloon disappears. (00:12:50)
The Sandman Cometh (1) - S2-E33
Continuity mistake: As the batfight ends and one of Sandman's henchmen hits Batman with a bolt of cloth, he goes down and is buried with mattresses on the right side. But when they remove the mattresses to wake him up, he is facing forward.
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 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.
The Zodiac Crimes (1) - S2-E37
Continuity mistake: Joker's floating zap-wand is hanging in the air right in front of Chief O'Hara's face. But when the shot cuts, it's instantly ten feet away, and is now floating behind the Joker. (00:01:45)
The Zodiac Crimes (1) - S2-E37
Continuity mistake: In Commissioner Gordon's office, after Batman uses his handy mini fire extinguisher to extinguish Joker's flaming 2-way spy device, when he walks over to Gordon's desk the mini fire extinguisher is in his left hand, but when it cuts to the closeup as he realises the significance of RAM, the fire extinguisher is suddenly in his raised right hand. (00:06:50)
The Zodiac Crimes (1) - S2-E37
Continuity mistake: Robin is holding an upright 8-foot pole when Venus sprinkles her knock-out glitter on the Dynamic Duo. When the shot cuts and they fall to the floor, the pole has completely disappeared. (00:22:10)
The Joker's Hard Times (2) - S2-E38
Continuity mistake: At GCPD HQ, when Commissioner Gordon decides to call Batman he removes the Batphone's acrylic dome cover and lifts the red receiver, still holding it when Joker shows up. Then, when Joker announces his next target is Libra the scales, in the next shot from a different angle, the Batphone is now untouched under the acrylic dome, between shots. (00:02:55)
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