Penguin Is a Girl's Best Friend (1) - S2-E42
Visible crew/equipment: While Batman and Robin are at the studio, Harriet and the others from the Gotham City League of Film Decency confront Penguin about scene 12. When Harriet says, "This scene is bursting with other things as well," there's a shot facing Marsha with two other women, and we can see a curved chalk mark at Marsha's feet and a chalk T-mark at the other woman's feet. (00:13:20)
Visible crew/equipment: When the museum closes early and Joker calls to each of his cohorts, their individual chalk T-marks are visible on the floor where they all stand. (00:12:40)
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)
The Devil's Fingers (1) - S2-E15
Visible crew/equipment: When Commissioner Gordon calls Chandell to reassure him that Batman and Robin are back in action, Chandell shares more root beer with Harriet. Then, when he hints for her to leave, a T-mark taped to the floor is visible at the lower left side of the screen. (00:18:20)
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)
Batman Makes the Scenes (2) - S1-E34
Revealing mistake: While Batman and Robin are being held in Penguin's vacuum room, some of the stunt's dark squibs attached to the balloons become visible during this scene. We can even see a squib spark on the last pink balloon. (00:02:15)
The Foggiest Notion (2) - S3-E12
Visible crew/equipment: When Batgirl enters the cricket pavilion at Ffogg Place, two chalk T-marks are visible on the floor between the snuffboxes case and the diamonds case. (00:11:35)
The Zodiac Crimes (1) - S2-E37
Visible crew/equipment: Bruce Wayne and Dick Grayson walk into the study alone when Bruce takes the Batphone call from Commissioner Gordon, then just as Bruce says, "The Joker again," at the top of the tuba bell we can see the reflection of a man wearing a white short-sleeved shirt and grey pants. Numerous studio lights are reflected as well. (00:03:15)
The Joker's Hard Times (2) - S2-E38
Continuity mistake: After Joker enters Commissioner Gordon's office, Gordon and Chief O'Hara walk over to the window, and the Batphone table is behind them, beside Gordon's desk. Then Joker makes two "quick-frozen cops" and runs off to snatch Justice, leaving Gordon and O'Hara immobile. When their shock paralysis wears off, Gordon and O'Hara rush over to Gordon's desk, but the Batphone table and the Batphone have vanished (note the rug's pattern). (00:03:00 - 00:04:55)
The Joker's Hard Times (2) - S2-E38
Visible crew/equipment: After Joker and his henchmen steal the statue, it cuts to Commissioner Gordon and Chief O'Hara as they recover from their shock paralysis, and when they walk over to Gordon's desk, the wheel of filming equipment is visible at the right side of the screen. (00:04:55)
A Riddle a Day Keeps the Riddler Away (1) - S1-E11
Visible crew/equipment: After the opening credits, during the scene in Commissioner Gordon's office Gordon tells Chief O'Hara to assign an extra squad, and numerous white tape marks are visible on the rug as the actors walk around. (00:06:15)
The Joker's Hard Times (2) - S2-E38
Revealing mistake: When Joker pays another visit to Commissioner Gordon and Chief O'Hara, Joker's holding his wand, and in the shots from outside the GCPD office window we can see the wire cable dragging behind Joker, which is attached to the wand and providing its power. During these shots, the actors' small white tape markers are also visible on the rug, beside the Batphone table. (00:03:00)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: The tiny spider microphone rests on the back of Robin's right hand, but the close-up shows a gloved left fist. (00:20:55)
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