Continuity mistake: When Robin parks the Batmobile while Batman heads into the disco, Robin raises the radar antenna on the hood to spin and provide a good signal. But in the shot from behind Robin, as he lifts the dash Batscope cover, the radar antenna is still in its original position and hasn't been raised, but the Batscope visuals are working perfectly. It happens again, when Robin watches on the Batscope as Batman begins to collapse from the spiked OJ, the radar antenna hasn't been raised at all. (00:16:50)
Batman Stands Pat (2) - S1-E14
Visible crew/equipment: When the Dynamic Duo trace Turkey's bowler to Mad Hatter's lair, they proceed to climb the wall. Then Hatter tells his goons to get into place for the trap, and in the next overhead shot there's a white chalk T-mark on the floor near Mad Hatter, at the right side of the screen. (00:17:45)
When the Rat's Away the Mice Will Play (2) - S1-E12
Visible crew/equipment: While Robin is "fiddling with the atomic pile" up on the scaffolding in the Batcave, Commissioner Gordon calls Batman to ask if he'd been to Gordon's office earlier, and in the overhead shot of Gordon's office there are two white tape marks visible under the desk, with one at Gordon's feet. (00:17:45)
Fine Finny Fiends (1) - S1-E33
Visible crew/equipment: When Batman and Robin enter Penguin's hideout at the South Pier, with Penguin and his goons ready and waiting for them, the duo walk to the table and both of their chalk marks (a bit smudged) are visible on the floor where each stands. Then, when Penguin captures Robin and places him against the wall, another two chalk marks are visible on the floor for each actor. (00:20:40 - 00:22:05)
The Riddler's False Notion (2) - S1-E32
Visible crew/equipment: When Commissioner Gordon apologizes to Batman, the Caped Crusader tells Gordon to be careful from whom he accepts free lemonade, and during this conversation the reflection of the boom pole/mic is visible on the Batmobile's windshield. (00:03:40)
While Gotham City Burns (2) - S1-E30
Continuity mistake: While Bookworm is at stately Wayne Manor he hands Aunt Harriet a book, and when she opens it Harriet and Alfred are gassed unconscious. In the next closeup of the rare book encased in glass, its open pages have colorful illustrations, but in the next shot the open pages have only plain text. (00:09:30)
While Gotham City Burns (2) - S1-E30
Visible crew/equipment: After Gotham City PD show up at the giant cookbook with the Dynamic Duo trapped inside, when Gordon, O'Hara, and the officers are standing at the cookbook's cover, the chalk T-mark and other chalk marks are visible on the ground. (00:15:50)
The Bookworm Turns (1) - S1-E29
Visible crew/equipment: When Printer's Devil contacts Bookworm headquarters, just as he messages "plot A washout" Bookworm walks over to the desk, and the white tape mark is visible on the rug where Lydia will stand. (00:07:25)
The Pharaoh's in a Rut (2) - S1-E28
Visible crew/equipment: After Tut's henchmen carry "Bruce" from the mansion, Robin tells Alfred to meet him in the Batcave, and as Alfred walks toward the foyer a crew member is visible past the doorway, at the left. (00:11:30)
The Joker Trumps an Ace (1) - S1-E25
Revealing mistake: In Commissioner Gordon's office, when Batman opens Joker's gift the genie figure begins to inflate, and in the overhead shot the stunt's covered air hose is visible at the bottom of the screen. In the next shot Batman pops the figure causing it to deflate, and the wire at the top of the figure's head is visible as it descends. (00:07:05)
Visible crew/equipment: Outside Madame Soleil's, when Riddler notices the Batmobile he rushes up to it with Tallow following behind, and the chalk T-mark is visible on the ground at Tallow's feet. As this shot continues, when Tallow warns Riddler about the Batmobile's burglar alarms, the reflection of the boom pole/mic is visible on the glass. (00:19:10)
Revealing mistake: While Batman and Robin are tied up and suspended over the enormous candle dipper vat, there are stunt wires leading to under their capes. (00:21:00)
Better Luck Next Time (2) - S1-E20
Revealing mistake: When Batman dodges the tiger by using metal claws to climb the wall, the stunt wires lifting him are visible. (00:03:00)
Better Luck Next Time (2) - S1-E20
Visible crew/equipment: While Batman uses his metal claw to hang from the wall, he reverses his communicator's polarity and increases the audio modulation. It then cuts to the tiger, and at the start of this shot we can see the animal trainer's red gloved hand, at the bottom left corner of the screen. (00:04:40)
Better Luck Next Time (2) - S1-E20
Continuity mistake: While Batman is increasing his communicator's audio modulation so as to incapacitate the tiger, Batman is wearing Bat Ear Plugs to protect his hearing. As Batman turns his head in the closeup, we're able to see that the Bat Ear Plug has vanished from his right ear, then it reappears in its proper place. (00:04:55)
The Purr-Fect Crime (1) - S1-E19
Visible crew/equipment: When Commissioner Gordon uses the Bat Phone and Alfred answers, it then cuts to Bruce and Dick playing crazy chess, and as the camera moves for its dolly shot, two of the crew's wood planks with marks become visible on the floor. (00:02:15)
The Purr-Fect Crime (1) - S1-E19
Deliberate mistake: At the end, Batman chooses the button on the right which opens the door on the right, with the tiger inside, but the last shot of the episode has been flipped, so the tiger exits from the door on the left. (00:23:25)
The Purr-Fect Crime (1) - S1-E19
Revealing mistake: In the last shot of the episode, when the tiger exits the small room in the flipped shot, right at the end of this shot as the tiger jumps up, at the top of the screen we can see that the camera has been positioned under a platform for this tiger stunt. (00:24:15)
Deliberate mistake: When Batman and Robin get free from the train tracks in the nick of time, the shot of the couple on the passing train is flipped; note things are backwards. (00:04:30)
Visible crew/equipment: At the end Harriet surprises Bruce and Dick with a rehabilitated criminal, and when Blaze walks in we can see the shadow of the moving boom mic on the left side of the screen. (00:23:05)
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