Revealing mistake: To free himself from the Joker's goons, Batman throws a gas capsule on the floor. Two things; first, the Joker is instantly asphyxiated by a lot of smoke, but when the henchmen let Batman go in the next shot, the puff of colored fumes has barely started to rise, and the Joker is further away. Second, the capsule that Adam West throws with panache on the ground and that should generate the noxious cloud can be seen actually bouncing back up after his energetic toss. (00:15:30)
Continuity mistake: When Joker shows off for the first time his utility belt, it switches sides between shots. First each pocket has its buckle on the right, towards the blonde bimbo, then in close-up the buckles are on the left, and when it switches back to a wider angle, again they are on the right. (00:16:45)
Continuity mistake: The Joker sends a doll crashing through the window of Commissioner Gordon's office. O'Hara is holding in close-up the doll in a different way from the wider shots, and the jester cap of the figurine is also blatantly folded in a different fashion. (00:18:30)
Audio problem: Joker's TV debut as an opera singer isn't very convincing. Even through the partially-obscuring clown mask, you can see that his lips aren't moving at all. (00:22:30)
Visible crew/equipment: At the end, Joker announces the unmasking of Batman and Robin, then when Joker turns and walks toward them, multiple chalk T-marks are visible on the floor where the dynamic duo are being held. (00:23:55)
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.
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.
Continuity mistake: Everytime the Joker is shown on TV his hair is brown, but before and after the broadcasts, it's his usual green with no time for him to change it.
Other mistake: The Joker's escape is so cartoonish and ridiculous you wouldn't even know where to start; besides the fact that the explosion somehow engulfs instantly the whole baseball field, the guard on top of the wall is following his movement with the gun, so he sees the Joker, therefore the smoke screen is useless, not more effective in any way than the mere surprise of a coil suddenly springing up from the ground.
Continuity mistake: Batman's utility belt is normal in the beginning, but suddenly has a triple sized compartment when Batman goes to get up on the catwalk with his rope. (00:03:30)
Revealing mistake: Right at the end of the obligatory Bat-rope climb scene, look at Robin's cape; the wire that is used to keep it in place (aka sticking out to make it look like it is subjected to gravity and drapes down) loses position too soon, so the real gravity causes the cloth to go towards the wall the dynamic duo is supposedly walking vertically on. (00:11:30)
Continuity mistake: When Batman and Robin scale the warehouse wall then watch Joker and his cohorts, each of the two windows have latches at the bottom, but when the Dynamic Duo burst in through the window, only the left window has a latch. (00:11:45)
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)
Revealing mistake: The newsreel shows several issues of the imaginary Gotham City Times. Nice job with the headlines and the page layout, but every single one of them is issue number 11. (00:14:00)
Visible crew/equipment: After Joker reveals to his cohorts that his plan involves champagne, when it cuts to Commissioner Gordon standing with Batman at the microphone, as the camera zooms out the chalk T-mark is visible on the floor in front of Batman and another actor's mark in front of Chief O'Hara. (00:18:15)
Continuity mistake: During the climactic fight, Batman tosses the Joker utility belt, causing confetti and streamers to fall down all over the place in some shots, while there is no such paper rain in others. (00:21:40)
Visible crew/equipment: At the diamond exchange, when Mr. Freeze and his goons are by the wall safe, the shadow of the boom mic is visible in the top right corner of the screen. (00:13:50)
Other mistake: When Mr. Freeze is moving through the room evaluating the diamonds, the tanks on his back can be fire extinguishers. There is no way that the "weapon" attached by hose to them will work, as the handles have to be squeezed to discharge.
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.
Other mistake: During the final fight scene between the SOCK and POW, Mr. Freeze can be seen in the 76-degree heated section.
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