Continuity mistake: When Okie Annie shoots the chandelier over Batman and Robin, they both are dazed by it. But Shame only whacks Batman over the head with the chair before he falls unconscious. Robin is still waving his hands reacting to the chandelier fall and finally falls unconscious when Batman goes to the ground.
Revealing mistake: In the recap, in the wide shot where Mr Freeze uses his freeze gun on Batman and Robin, you can see they are stunt doubles.
Batman Stands Pat (2) - S1-E14
Revealing mistake: As Batman is about to use his batarang to Mad Hatter's hideout, right before getting caught by him and his henchmen towards the end of the episode, as he moves his cape back, the back part of his costume is open.
Revealing mistake: In this episode and the next one, Robin's stunt double is very obvious from the back, especially in the scene where they enter the Hall of Fame museum.
Batman Makes the Scenes (2) - S1-E34
Visible crew/equipment: When Penguin and his fine finny finks return to South Pier with the umbrella filled haul, just as Penguin tosses money at his henchmen, we can see the chalk T-mark on the floor under the table. (00:18:15)
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)
It's the Way You Play the Game (2) - S2-E26
Visible crew/equipment: At the Batcave, when Batman and Robin use the Batroscope it leads them to the Adobe Hacienda Motel and Eats, which serves the best chili and avocado dip in GC. When it cuts to them entering the building, at the start of this shot the shadow of the moving boom mic is visible in the bottom right corner of the screen. (00:09:30)
Visible crew/equipment: At the Gotham City Opera House, after the Terrific Trio have taken care of Shame and his men, Calamity Jan and Frontier Fanny show up and spray the heroes with fear gas. When Shame and his gang walk over to Batman, Robin, and Batgirl, a few chalk T-marks are visible on the floor where they will stand. (00:17:45)
Surf's Up! Joker's Under! - S3-E10
Revealing mistake: While Batman and Robin are being processed into the foam surfboard blanks, they are lying on two wood workbenches. When Riptide and Wipeout begin adding the coat of resin to both foam blanks, just as Riptide announces both blanks are smoking, we can see under Robin's wood workbench the fallen wired smoking apparatus used in the stunt. (00:13:05)
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)
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 Catwoman Goeth (2) (a.k.a. A Stitch in Time) - S2-E34
Visible crew/equipment: Outside the run down factory, when the GC police officers step out of their patrol car and walk over to the Batmobile, just as senior Officer Dietrich begins giving the rookie officer the what for, the reflection of the boom mic is visible on the Batmobile's left bubble windshield, at the left side of the screen. (00:10:50)
The Bird's Last Jest (2) - S2-E28
Visible crew/equipment: At the abandoned Navy rec center, when Penguin and his miscreants are out of bullets they surrender, and as they all gather with their hands up, there are a few chalk T-marks visible on the ground where they stand. (00:05:25)
Hizzonner the Penguin (1) - S2-E17
Other mistake: When Pengy shows up at the Grand Order of Occidental Nighthawks he feigns shock, then as he shoves his umbrella into the vat of sulfuric acid, Penguin moves his arm/hand toward the right to pull out a different umbrella, one that appears destroyed by the acid. (00:22:55)
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)
The Penguin Declines (3) - S2-E39
Revealing mistake: At the Batcave, when Penguin is up on the atomic pile scaffolding Batman grabs hold of him just as Pengy uses his umbrella to float down, and the stunt wire attached to the umbrella ferrule is visible while the duo descend together. (00:21:05)
The Thirteenth Hat (1) - S1-E13
Visible crew/equipment: When Hatter is at Octave Marbot's studio posing as him, Batman and Robin arrive, and chalk T-marks are visible on the floor near Batman's statue in the studio. Then while Batman is in the dressing room, Hatter quietly opens the studio's front door, and more chalk T-marks are visible on the floor in the hall. (00:18:40)
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)
Batman Stands Pat (2) - S1-E14
Visible crew/equipment: When Batman and Robin use the Batmobile's Detect-a-scope to locate Turkey's bowler, as Batman notes that Hatter's hideout must be in the old warehouse, the reflection of the boom pole/mic is visible at the right side of the Batmobile's bubble windshield. (00:16:55)
The Entrancing Dr. Cassandra - S3-E25
Visible crew/equipment: While Batman and Robin are at GCPD, Batman decides to use the library to research occult sciences, and when it cuts to Cassandra and Cabala returning to their hideout they walk over to the table, and behind them we can see the chalk marks on the floor by the door, where they previously stood. (00:05:15)
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