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)
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)
Visible crew/equipment: When both Batman and Robin realise that even though the museum can't be broken into, it doesn't mean someone couldn't break "out" of the museum, as they rush to the museum's front doors we can see a chalk T-mark on the ground in front of the doors. (00:13:25)
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)
The Penguin's a Jinx (2) - S1-E4
Revealing mistake: When Penguin uses the large umbrella on his penguin line to slide across to Dawn's penthouse terrace, as he says, "Who says penguins can't fly," we can see the glistening of the crew's wire at the top of the pulley wheel, as it moves. (00:13:45)
The Penguin's a Jinx (2) - S1-E4
Visible crew/equipment: When Penguin is riding the large umbrella across the Penguin line in the wide shot, just as he is about to reach Dawn's terrace, we can see a crew member's two arms reaching out to Penguin and the top of a ladder, at the lower left side of the screen. (00:13:50)
The Penguin's a Jinx (2) - S1-E4
Revealing mistake: When Penguin uses the large umbrella to slide across the Penguin line, at the top of the umbrella there's a pulley wheel, but when he reaches Dawn's penthouse terrace there's only a small loop at the top of the large umbrella. The same thing happens when Swoop follows Penguin on another large umbrella. (00:13:40)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: At the start, Penguin's henchmen give out booby trapped umbrellas to everyone outside the House of Ali Baba. When they all enter the jewelry store those umbrellas explode with fireworks, gas, confetti, etc, and the stunt wires holding up the umbrellas are visible, at the top of the screen. (00:01:20)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: After the huge rooftop umbrella is launched onto the street there's a small umbrella hanging from its handle, and when Batman uses his Batarang to swing towards the huge umbrella's shaft, his stunt wires are visible. (00:18:45)
Fine Feathered Finks (1) - S1-E3
Visible crew/equipment: In Commissioner Gordon's office, when Gordon is looking over the paperwork of three new umbrella factories, frustrated that none are in the name of Penguin, as he stands up we see two white tape marks on the rug behind him. In the previous scene with Warden Crichton, four of the actors had been standing in that area. (00:11:35)
Continuity mistake: When Robin has the idea that Riddler placed two other riddles hidden in the legal documents, Robin holds the papers up with his raised right hand, but in the next shot the documents are being held up in Robin's left hand. (00:13:45)
Continuity mistake: At the secret HQ of the Mole Hill Mob, Molly is wearing a ring on her right hand and many bangle bracelets as she dances, but in the closeup when reaches into the caviar jar the ring and bracelets are gone, then it all reappears. (00:15:00)
The Funny Feline Felonies (1) - S3-E16
Other mistake: At the start of the episode, Bruce Wayne and Warden Crichton are overseeing Joker's release from prison, but at the tail end of the last episode, Batman is shocked that Joker is released from jail. He could not be two places at once.
Other mistake: The opening scene and dialogue with Bruce and Dick responding to Gordon's call is from The Curse of Tut.
He Meets His Match, the Grisly Ghoul (2) - S1-E16
Other mistake: During the opening scene, right after Cesar Romero's guest star, Joker and Susie's faces freeze for a moment.
Batman Stands Pat (2) - S1-E14
Other mistake: When Batman drop-kicks Mad Hatter into the vat of acid at the end of the fight, he does not have even one burn mark when he was pulled out.
The Minstrel's Shakedown (1) - S2-E5
Plot hole: When Batman and Robin explain to the board members at the stock exchange that Minstrel will not be a threat because they dealt with Penguin, Archer, Clock King, King Tut, and Catwoman, in broadcast order, there is a 6-episode difference between Minstrel and Clock King who has never been seen before. To the first-time viewer, they were probably wondering who Clock King is.
Shoot a Crooked Arrow (1) - S2-E1
Continuity mistake: When Batman and Robin are ensnared by Archer's net, Batman says he will get his batknife to free them. When Archer shoots them down with the arrow, they are apparently unconscious but with no explanation of what knocked them out while stuck in the net.
Other mistake: During the final fight scene between the SOCK and POW, Mr. Freeze can be seen in the 76-degree heated section.
Other mistake: While Batman and Robin are pursuing False Face, they stop the Batmobile beside a fence (across from "Bioscope"), and a sign that states "No Trespassing, Desilu Studios" (the show's studio location) is mounted on that fence. (00:15:00)
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