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)
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: 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)
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)
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.
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)
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)
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)
Continuity mistake: When Batman and Robin crash through the window, there's no glass left in the frame - at least not until the next shot, when several large shards that weren't there before suddenly appear at the edges. (00:11:50)
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)
Smack in the Middle (2) - S1-E2
Continuity mistake: Just after the Joker tells the fake Robin to turn on her homing beacon, a quick shot of the Batmobile approaching shows it isn't glossy black with cherise red trim as normal, but is instead flat black with white trim. This footage was from pre-series testing, painting the car different ways to see how it would look best on film, but somehow this footage was actually used in the episode by mistake. (00:06:20)
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 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 Riddler's False Notion (2) - S1-E32
Continuity mistake: When the Riddler has a blindfolded Robin out on the window ledge, the position of Robin's blindfold changes between shots, from covering his nose entirely to being just above it.
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)
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