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)
The Penguin Declines (3) - S2-E39
Continuity mistake: When Joker's goons return from Operation Laundry Bag and finally release Penguin from the bag, Penguin's hat is secured on his head with an elastic strap, but this strap vanishes in the next shot. (00:04:30)
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)
Batman's Satisfaction (2) - S2-E52
Continuity mistake: After Britt Reid tells Bruce he wouldn't be caught dead in Batman's crazy cowl, when it cuts to the Batcave both Robin and Batman use the Bat-computer to decipher the message in the alphabet noodle soup. The Yellow Pages phone book is on the computer's shelf beside Robin, and in his closeups the phone book's spine faces toward the right, but in the wide shots the phone book faces the opposite way. (00:10:30)
The Clock King's Crazy Crimes (1) - S2-E11
Continuity mistake: When Clock King steals his favorite painting from the gallery, as he places it through the wall hole note the strips of tape adhered to the paintings back, and its hanging wire near the bottom (it's upside down). In the next shot from the other side of the wall hole, the painting is now turned the opposite way (it's right side up), note the tape strips. (00:16:25)
The Clock King's Crazy Crimes (1) - S2-E11
Continuity mistake: During the fight in the art gallery, the papers on the desk to the left of the screen are scattered. But in some shots of the fight progressing, the same papers have straightened themselves back into nice, neat stacks again. (00:17:00)
Shoot a Crooked Arrow (1) - S2-E1
Continuity mistake: The arrow Archer fires into the window frame in Commissioner Gordon's office is, depending on the camera shot, angled up, then down, up, down and up again. (00:07:30)
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)
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)
Continuity mistake: Between takes at the end of the final fight scene, most of the chairs shift positions around the table, the wooden partition screen that fell over during the scuffle has somehow folded itself, and a white cloth that was draped over one of the chairs has disappeared. (00:22:00)
The Clock King Gets Crowned (2) - S2-E12
Continuity mistake: Batman tosses a large white box at one of the henchmen. The box lands on the round dais of the clockworks, but as that dais begins to rotate, the box disappears. It pops back up a few shots later, now sitting on the stationary corner of the clockwork platform. But as the fight rages on, it vanishes again between shots. (00:21:30 - 00:22:10)
The Minstrel's Shakedown (1) - S2-E5
Continuity mistake: When Alfred brings the lunch tray down to the Batcave, Batman is holding a soldering iron, working on the electronic bug. When the shot cuts to a close-up, the soldering iron vanishes, and he's holding a clear plastic probe instead. (00:10:15)
Continuity mistake: While Batman is telling Octavia that she can go free, his hands are either straight down at his sides or clasped together at chest level, depending on the shot. (00:06:15)
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)
Shoot a Crooked Arrow (1) - S2-E1
Continuity mistake: When the Archer robs Wayne Manor's safe, an unconscious Dick Grayson shifts positions on the floor between takes. At first, he's lying with both hands folded over his chest. A few shots later, his left arm is stretched out over his head. (00:01:30)
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 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)
Continuity mistake: Batman folds up the Bat Shield and starts to tuck it into his belt, which it is much too large to fit into. In the very next shot, the shield has disappeared. (00:21:00)
Continuity mistake: Tied to a conveyor belt, Batman and Robin move past a stack of boxes stenciled with the factory's name. Cut to close-up, and they're now back to a position right next to the boxes. Back to master shot, and the boxes are once again several feet away - at least until the next close-up. (00:02:50)
Continuity mistake: As Tut prepares to re-animate the scarab beetles, his apothecary henchman stands to his immediate right, close enough to touch his shoulder. But when the shot cuts to a wider angle, the man is standing a foot away. (00:08:45)
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