Revealing mistake: While Batman and Robin are tied up and suspended over the enormous candle dipper vat, there are stunt wires leading to under their capes. (00:21:00)
Better Luck Next Time (2) - S1-E20
Revealing mistake: When Batman dodges the tiger by using metal claws to climb the wall, the stunt wires lifting him are visible. (00:03:00)
Better Luck Next Time (2) - S1-E20
Visible crew/equipment: While Batman uses his metal claw to hang from the wall, he reverses his communicator's polarity and increases the audio modulation. It then cuts to the tiger, and at the start of this shot we can see the animal trainer's red gloved hand, at the bottom left corner of the screen. (00:04:40)
Better Luck Next Time (2) - S1-E20
Continuity mistake: While Batman is increasing his communicator's audio modulation so as to incapacitate the tiger, Batman is wearing Bat Ear Plugs to protect his hearing. As Batman turns his head in the closeup, we're able to see that the Bat Ear Plug has vanished from his right ear, then it reappears in its proper place. (00:04:55)
The Purr-Fect Crime (1) - S1-E19
Visible crew/equipment: When Commissioner Gordon uses the Bat Phone and Alfred answers, it then cuts to Bruce and Dick playing crazy chess, and as the camera moves for its dolly shot, two of the crew's wood planks with marks become visible on the floor. (00:02:15)
The Purr-Fect Crime (1) - S1-E19
Deliberate mistake: At the end, Batman chooses the button on the right which opens the door on the right, with the tiger inside, but the last shot of the episode has been flipped, so the tiger exits from the door on the left. (00:23:25)
The Purr-Fect Crime (1) - S1-E19
Revealing mistake: In the last shot of the episode, when the tiger exits the small room in the flipped shot, right at the end of this shot as the tiger jumps up, at the top of the screen we can see that the camera has been positioned under a platform for this tiger stunt. (00:24:15)
Deliberate mistake: When Batman and Robin get free from the train tracks in the nick of time, the shot of the couple on the passing train is flipped; note things are backwards. (00:04:30)
Visible crew/equipment: At the end Harriet surprises Bruce and Dick with a rehabilitated criminal, and when Blaze walks in we can see the shadow of the moving boom mic on the left side of the screen. (00:23:05)
Continuity mistake: When False Face escapes from the bank he has Blaze with him in the Town Panel truck, and she's handcuffed to the overhead pipe. Blaze is wearing a neutral color nail polish, but in the closeups of her cuffed hand her nail polish is salmon colored. (00:14:30)
Batman Stands Pat (2) - S1-E14
Visible crew/equipment: Batman and Robin have been captured so they're led to Mad Hatter's hat factory. When Lisa arrives, a chalk mark can be seen where she stands, and a white tape mark on the floor for Mad Hatter. (00:19:30)
When the Rat's Away the Mice Will Play (2) - S1-E12
Visible crew/equipment: While Bruce Wayne is in Commissioner Gordon's office, when the Batman imposter shows up, numerous white tape marks are visible on the rug, where the actors will step as the scene progresses. (00:14:20)
When the Rat's Away the Mice Will Play (2) - S1-E12
Visible crew/equipment: After the Batman imposter has met Bruce Wayne in Commissioner Gordon's office, when it cuts to the imposter returning to Riddler's hideout, the chalk T-mark and another mark are visible on the floor near Mousey's feet. (00:16:25)
When the Rat's Away the Mice Will Play (2) - S1-E12
Revealing mistake: When Riddler and his Rats have been caught near the end, during the ensuing fight Batman throws one of the Rats, and as he goes flying across the room we can see the stunt wires. (00:21:55)
A Riddle a Day Keeps the Riddler Away (1) - S1-E11
Visible crew/equipment: While King Boris is being held as a pawn by Riddler, when Batman and Robin show up the duo jump over a crate, and the chalk T-mark is visible on the floor by Robin's feet. (00:21:05)
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)
A Riddle a Day Keeps the Riddler Away (1) - S1-E11
Visible crew/equipment: After Batman tells Robin to look up the address for the Royal Mushroom Club, when it cuts to Riddler's hideout a chalk T-mark can be seen on the floor near the wall opening, where Mousey will stand in a moment. (00:12:15)
A Death Worse Than Fate (2) - S1-E10
Visible crew/equipment: When Zelda releases blindfolded Harriet at the street corner, there are two curved chalk actors' marks on the ground beside Harriet's feet. (00:08:35)
A Death Worse Than Fate (2) - S1-E10
Visible crew/equipment: After the opening credits, in Commissioner Gordon's office, a white tape mark is visible on the floor near the corner of Gordon's desk, where Chief O'Hara is sitting, then Gordon walks over to his mark. (00:02:55)
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)
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