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 Thirteenth Hat (1) - S1-E13
Continuity mistake: When Batman parks the Batmobile in front of Octave Marbot's studio, Batman tells Robin to activate the vehicle's anti-theft device. Robin is wearing green leather gloves, but in the closeup Robin's green glove is made out of a material (looks like cotton) very different than Robin's gloves. (00:18:15)
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)
Continuity mistake: When Batman and Robin are in the museum speaking with the director, Batman's chest emblem is high enough on his chest that it nearly touches the bottom edge of his cowl. In the next shot, when he leaves the museum, the emblem has moved down several inches.
Batman Stands Pat (2) - S1-E14
Continuity mistake: Batman's plaster-covered costume gets an instant dry cleaning en route as he drives from the sculptor's studio to the batcave. (00:05:00)
Batman Stands Pat (2) - S1-E14
Continuity mistake: When Batman and Robin break through Mad Hatter's window, several large chunks of glass remain attached to the wood frame. In the very next shot, they've vanished. (00:18:00)
Continuity mistake: While the unconscious Robin is being carried away from the Batmobile by one of Riddler's thugs, his cape loosens and appears to completely fall off just before they exit the frame. In the next shot, Robin is still being carried away but his cape is securely back in place.
Smack in the Middle (2) - S1-E2
Continuity mistake: Molly is about to disguise herself as Robin. But the wig she's holding isn't even remotely the same color as Robin's hair. Of course, as soon as she puts it on and transforms herself, the wig darkens and becomes Robin's actual hair. (00:05:45)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: When Batman reverses direction of the Batmobile via a "Bat-Turn", the car is shown from above turning counter-clockwise, but the next interior view shows the car is spinning clockwise. (00:14:20)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: When Batman starts the Bat-Turn, the parachutes are shown deploying on a 6-lane major roadway (3 lanes in each direction) in a very open area, but after completing the 180-degree turn, the car is shown driving away from the crumpled chutes on a much narrower side street among tall buildings. (00:14:10)
The Joker Goes to School (1) - S1-E15
Continuity mistake: In the batcave, Batman's cape suffers a case of over-the-shoulder/off-the-shoulder blues, going from one to the other several times between takes. (00:19:10)
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)
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)
Continuity mistake: While Bruce Wayne is lying on a gurney at the back of the ambulance, in the wide shot of Tut's henchmen driving along on the street, there's a rearview mirror on the windshield and a single beacon light on the roof, but in the closeups the rearview mirror is gone and there are two beacon lights on the roof. (00:21:30)
Continuity mistake: When False Face escapes from the bank he has Blaze with him in the Town Panel truck, and she's handcuffed to the overhead pipe. Blaze is wearing a neutral color nail polish, but in the closeups of her cuffed hand her nail polish is salmon colored. (00:14:30)
Continuity mistake: At the secret HQ of the Mole Hill Mob, Molly is wearing a ring on her right hand and many bangle bracelets as she dances, but in the closeup when reaches into the caviar jar the ring and bracelets are gone, then it all reappears. (00:15:00)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: When the Penguin goes to Wayne Manor to put Batman and Robin to sleep with the gas from his umbrella, just before he shoots the orange gas at Robin's suit of armor, there's a quick shot of the armor's helmet. The problem is that there's already an orange stain on the face of the helmet from the orange gas that comes out of the tip of the umbrella, even before Penguin shoots any gas. (00:19:15)
Batman Stands Pat (2) - S1-E14
Continuity mistake: At the end, as Bruce Wayne speaks to Magda, he's standing with his arms at his sides. When the shot cuts, his hands are suddenly clasped in front of him. (00:23:30)
Continuity mistake: In close-up, Bruce Wayne folds his newspaper in half, leaving the folded edge facing the camera. The shot cuts to a wider view and immediately, the paper has reversed positions in his hand. (00:04:00)
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