The Impractical Joker (1) - S2-E21
Continuity mistake: Toward the end of the fight in the fur salon, one of Joker's henchmen shifts locations instantaneously. In the first shot, he's on the far side of Robin, falling against the wall. In the very next shot, he jumps to a spot between Robin and the camera, where he takes a swing at Batman. (00:17:00)
The Yegg Foes in Gotham (2) - S2-E14
Visible crew/equipment: During the final egg fight, the microphone shadow puts in an appearance on the wall behind the bad guys. (00:21:50)
Visible crew/equipment: When Harry plots to replace Chandell, the polished grand piano behind him reflects the moving lights on some of the studio equipment. (00:15:30)
Factual error: King Tut is said here to have been a 4th Dynasty ruler. Just as in the previous Tut episode, Egyptian history seems to have entirely escaped Batman's writers. They previously mis-identified Tut's namesake as a 14th Dynasty ruler, and this time around, guessed wrong again. In fact, Tutenkamen's brief rule was part of the 18th Dynasty. (00:03:30)
Shoot a Crooked Arrow (1) - S2-E1
Continuity mistake: When the Archer robs Wayne Manor's safe, an unconscious Dick Grayson shifts positions on the floor between takes. At first, he's lying with both hands folded over his chest. A few shots later, his left arm is stretched out over his head. (00:01:30)
The Zodiac Crimes (1) - S2-E37
Continuity mistake: Joker's floating zap-wand is hanging in the air right in front of Chief O'Hara's face. But when the shot cuts, it's instantly ten feet away, and is now floating behind the Joker. (00:01:45)
The Greatest Mother of Them All (1) - S2-E9
Revealing mistake: When Ma Parker activates her jet-propelled wheelchair, the much younger stunt woman's face is visible as the chair speeds down the hallway toward Batman and Robin. (00:09:15)
The Puzzles Are Coming (1) - S2-E31
Continuity mistake: In the Batcave, Batman is holding Puzzler's pink balloon while he and Robin deduce its clues. The shot cuts to a wider angle when they turn to race to the Batmobile, and the balloon disappears. (00:12:50)
The Joker's Provokers (2) - S2-E22
Factual error: Tsk. After all his lectures to Robin about the importance of education, Batman should and would know better. On the chalk board, where he's written out Joker's message (dictated to him over the phone), the caped crusader mis-punctuates the phrase "a gargoyle's key" by leaving out the apostrophe. Definitely not a mistake that stickler-for-correctness Batman would make. (00:09:30)
Continuity mistake: Batman folds up the Bat Shield and starts to tuck it into his belt, which it is much too large to fit into. In the very next shot, the shield has disappeared. (00:21:00)
Continuity mistake: Tied to a conveyor belt, Batman and Robin move past a stack of boxes stenciled with the factory's name. Cut to close-up, and they're now back to a position right next to the boxes. Back to master shot, and the boxes are once again several feet away - at least until the next close-up. (00:02:50)
Continuity mistake: As Tut prepares to re-animate the scarab beetles, his apothecary henchman stands to his immediate right, close enough to touch his shoulder. But when the shot cuts to a wider angle, the man is standing a foot away. (00:08:45)
Continuity mistake: Mr. Freeze has frozen the commissioner's office, and when Batman applies plastic explosive to the door, a frost stripe appears that wasn't there in the master shot a moment before. In the next shot, the putty he's just put there disappears. And when the explosion occurs (even though Batman didn't add any detonators), it doesn't emanate from anywhere near the spot where he applied the putty. (00:06:00)
Tut's Case is Shut (2) - S2-E8
Continuity mistake: Tut's "pets," which are a little too obviously plastic, are crocodiles (with pointed snouts), and they're sitting on a grassy island in their water tank. The stock footage inserts, however, are of alligators (which have flat snouts) swimming in open water, with no island in sight. (00:02:30)
The Penguin's Nest (1) - S2-E27
Revealing mistake: When Bruce, Dick and Aunt Harriet get into what's supposed to be an elevator, there's solid concrete under the sliding doors where there should be a break separating the lift car from the building's floor. It's visible again in Part 2, when Batman and Robin use the same elevator. (00:04:30)
The Clock King Gets Crowned (2) - S2-E12
Continuity mistake: Batman and Robin are trapped in the overturned hourglass. They're sitting upright when Batman suggests an escape plan. In the very next shot, they're sprawled face down on the sand. (00:04:15)
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 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 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)
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