Other mistake: After King Tut's men deliver the statue, it's referred to as a Sphinx. Even Batman says, "Rather good imitation of the 4th Dynasty's Sphinx at Giza." Problem is, the Great Sphinx of Giza is a reclining lion with a human head. The statue in Gotham's park is a ram's head atop a seated human body, resembling Egyptian God Khnum, and looks nothing like the Egyptian Sphinx. Bruce Wayne is a member of Gotham City Museum's Board of Trustees, which recently opened the new exhibit of Egyptian antiquities. (00:10:35)
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.
Batman Stands Pat (2) - S1-E14
Continuity mistake: Batman's plaster-covered costume gets an instant dry cleaning en route as he drives from the sculptor's studio to the batcave. (00:05:00)
Revealing mistake: Most of the first season's episodes follow a standard outline where, after the opening credits, Batman and Robin arrive in the Batcave via the Batpoles, run and enter the Batmobile and drive off, along the winding, dusty roads toward Gotham, then arrive in front of City Hall, exit the car and run up the stairs. But very quickly it becomes obvious that every bit of this is the same footage used over and over. As they get in the car, it's on a black platform which vanishes as the car starts moving. The same cloud of dust appears as the car's rear heads into the distance on the winding road, and the same crowd of people are in front of City Hall, nearly every episode.
Batman Stands Pat (2) - S1-E14
Continuity mistake: When Batman and Robin break through Mad Hatter's window, several large chunks of glass remain attached to the wood frame. In the very next shot, they've vanished. (00:18:00)
The Joker Goes to School (1) - S1-E15
Revealing mistake: Batman drives out of the batcave alone. The first bit of stock footage of the car leaving the cave does indeed show him alone in the batmobile. But the very next stock shot of the car speeding down the dirt road shows us Robin sitting in the passenger seat. (00:05:25)
Continuity mistake: While the unconscious Robin is being carried away from the Batmobile by one of Riddler's thugs, his cape loosens and appears to completely fall off just before they exit the frame. In the next shot, Robin is still being carried away but his cape is securely back in place.
When the Rat's Away the Mice Will Play (2) - S1-E12
Visible crew/equipment: The microphone dips into the shot at the end, just as Aunt Harriet is kissing Dick and Bruce good-bye. (00:23:20)
Smack in the Middle (2) - S1-E2
Continuity mistake: Molly is about to disguise herself as Robin. But the wig she's holding isn't even remotely the same color as Robin's hair. Of course, as soon as she puts it on and transforms herself, the wig darkens and becomes Robin's actual hair. (00:05:45)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: When Batman reverses direction of the Batmobile via a "Bat-Turn", the car is shown from above turning counter-clockwise, but the next interior view shows the car is spinning clockwise. (00:14:20)
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)
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)
Revealing mistake: The Batcave was a stage set with no real exit for the car. So in many episodes where a shot is looking into the cave from the darker tunnel as the Batmobile approaches and passes to our right, the rear end of the car jumps upward and tire skid marks appear on the floor as the driver slams on the brakes to avoid hitting the studio wall that is out of the shot, while the audio suggests the car is still accelerating.
Fine Feathered Finks (1) - S1-E3
Continuity mistake: When Batman starts the Bat-Turn, the parachutes are shown deploying on a 6-lane major roadway (3 lanes in each direction) in a very open area, but after completing the 180-degree turn, the car is shown driving away from the crumpled chutes on a much narrower side street among tall buildings. (00:14:10)
A Riddle a Day Keeps the Riddler Away (1) - S1-E11
Visible crew/equipment: During the first scene in Commissioner Gordon's office, the microphone shadow is outlined on the front of Chief O'Hara's uniform. (00:01:50)
The Joker Goes to School (1) - S1-E15
Continuity mistake: In the batcave, Batman's cape suffers a case of over-the-shoulder/off-the-shoulder blues, going from one to the other several times between takes. (00:19:10)
Smack in the Middle (2) - S1-E2
Deliberate mistake: Ignoring that its very unlikely all of Jill St. John's copious red hair would fit under a wig that passes for Robin's hair, it's impossible that it would emerge from under that wig looking as full and perfectly styled as it does when she's in the Batcave.
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)
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)
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