Visible crew/equipment: When Olga shouts, "Da, da, da! Drowning her in caviar!" in the overhead shot, the boom mic repeatedly dips into view over Olga, at the top of the screen. (00:21:55)
Visible crew/equipment: After Egghead dumps Batgirl into the vat of caviar, Egghead, Olga, and the Cossacks attempt to escape, then just as they run out the door, a bit of set lighting equipment (which wasn't in previous shots) is visible at the left side of the screen. (00:22:10)
Visible crew/equipment: While Batman and Batgirl are in the dungeon attempting to escape, it cuts to Alfred and Robin meeting up at the Batmobile at the same time, and the reflection of the diagonal boom pole is visible on the windshield. (00:16:15)
Revealing mistake: When Batgirl hands Batman the rope, just as he tells her to concentrate on the Indian fakir command, above Batman's head we can see the glistening wire that will be used in the stunt. Then, after Batman and Batgirl have escaped the dungeon Robin rushes up and asks how they did it, and when Batman reiterates the Indian fakir command for Robin, we can see the wire attached to the rope. (00:15:55 - 00:18:05)
Surf's Up! Joker's Under! - S3-E10
Visible crew/equipment: After Batman wins the competition, when Hot Dog is finally released from the trash can Joker rushes over to claim it was just a little joke, and the microphone pops up into view at the bottom of the screen. (00:21:10)
Surf's Up! Joker's Under! - S3-E10
Visible crew/equipment: After Batman and Robin head out to Joker's hideout, when it cuts to Joker upon his success at stealing all of Skip's talent and vigor, just as Joker says, "You know what this means boys, the surfing championship," we can see the shadow of the boom mic moving at the far right side of the screen. (00:09:50)
How to Hatch a Dinosaur (2) - S3-E9
Visible crew/equipment: While Batman and Robin are in Commissioner Gordon's office Barbara reports the theft of the Neosaurus egg, and when Batman suspects it's connected to the radium theft, he and Robin decide to use the Batcomputer at the Batcave. Just as the Dynamic Duo rush to Gordon's door the camera turns to follow them, and we can see filming equipment at the right side of the screen as it tries to move out of view. (00:09:55)
How to Hatch a Dinosaur (2) - S3-E9
Visible crew/equipment: After Egghead tells Olga he's planning a three-course meal for the Neosaurus consisting of Batman, Robin, and Batgirl, and for dessert - Commissioner Gordon and Chief O'Hara. Then it cuts to the Batcave as Batman talks about the Bat-geiger, and when the camera moves closer we can see the camera movement's reflection on the windshield, at the bottom right corner of the screen. (00:15:15)
Visible crew/equipment: At the start, Egghead and the Cossacks ride past two women, and they stop to watch, then when the camera zooms in on them the reflection of the moving boom pole/mic is visible on the glass window, at the top right side of the screen.
The Unkindest Tut of All - S3-E6
Deliberate mistake: When Batman has figured out King Tut's plot to steal ancient Egyptian scrolls from the Gotham City Library, he and Robin rush away, and in the shot of the library exterior, the words "The New York Public Library" is quite noticeable above the entryway. (00:18:00)
The Sport of Penguins (1) - S3-E4
Deliberate mistake: After the episode intro, in the first shot we see the words "The New York Public Library" above the entrance to the library, where Barbara Gordon works. However, it's stated in S3xE1 that she works at Gotham City Library, and even in this episode when Penguin listens to the news about the bomb, it's noted as the Gotham Library. (00:02:00)
Continuity mistake: Batgirl's outfit includes boots with kitten heels, but during the fight scenes the stuntwoman's boots have block heels. (00:19:45 - 00:21:25)
Ring Around the Riddler - S3-E2
Continuity mistake: When Batgirl finds Betsy with the huge magnet under the boxing ring Batgirl throws the rope around the lever, then as the rope pulls the lever down the rope slips off and falls, but in the next shot the rope is still up around the lever. (00:21:25)
Pop Goes the Joker (1) - S2-E57
Continuity mistake: After Oliver Muzzy congratulates Joker for his magnificent artwork and makes a deal with him, before Joker leaves the gallery he runs his finger across Batman's yellow emblem to sign his red artwork, but at GCPD HQ when they're discussing the matter, Joker's signature is completely different, it's now a capital "J" on Batman's yellow emblem. (00:06:45)
Caught in the Spider's Den (2) - S2-E56
Visible crew/equipment: In Commissioner Gordon's office, when Gordon and Chief O'Harah walk over to the Batphone so they can talk to Robin and get him to surrender, we can see the actor's white tape mark taped to the rug, just as Gordon removes the clear acrylic dome from the Batphone. (00:17:20)
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)
A Riddling Controversy (2) - S2-E46
Continuity mistake: When Riddler and his baddies are at their factory hideout watching the news of their criminal coup on TV, in shots facing the TV the two rabbit ear antenna are fully retracted, but in shots from behind the TV the antenna are extended by approximately a foot. Later, there's a similar occurrence with the TV antenna, while Batman and Robin use the Batrope to climb the wall. (00:03:20)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: While Penguin and all his goons are holed up in the sub-treasury vault, in the shots of Batman, Robin, Gordon, and O'Hara waiting for three days, assorted chalk marks are visible on the floor where some of the actors stand or will stand. (00:17:10)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: When Marsha is down to one veil she ends her dance, then as she and Aunt Hilda try to get away they're stopped by the love-sick sub-treasury guards, and there's a curved white chalk mark on the floor where Marsha stands. (00:12:05)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: When the Dynamic Duo follow the lizard trail and go down into the manhole they end up in Hilda's cave, and when they approach Penguin's goon standing by a door, there are two chalk T-marks on the floor near that door. (00:08:50)
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