Smack in the Middle (2) - S1-E2
Revealing mistake: While Riddler is with the unconscious guests at the Moldavian exhibit, in the basement of the Moldavian Pavilion the Mole Hill gang blow up the ceiling to create an entry to the exhibit, on the floor above. They lean two tall ladders at the side of the hole and climb up. When Riddler makes for an escape Batman follows him down below, and now we can see long metal brackets bolting the ladders to the floor for safety. (00:20:20 - 00:22:00)
The Thirteenth Hat (1) - S1-E13
Continuity mistake: When Batman parks the Batmobile in front of Octave Marbot's studio, Batman tells Robin to activate the vehicle's anti-theft device. Robin is wearing green leather gloves, but in the closeup Robin's green glove is made out of a material (looks like cotton) very different than Robin's gloves. (00:18:15)
While Gotham City Burns (2) - S1-E30
Visible crew/equipment: When Batman and Robin use the Batmobile's high energy radar to probe the giant cookbook, and also when they use the Bat-magnet, the reflection of the moving boom mic/pole is visible on the bubble windshield. (00:11:40)
Visible crew/equipment: Outside Madame Soleil's, when Riddler notices the Batmobile he rushes up to it with Tallow following behind, and the chalk T-mark is visible on the ground at Tallow's feet. As this shot continues, when Tallow warns Riddler about the Batmobile's burglar alarms, the reflection of the boom pole/mic is visible on the glass. (00:19:10)
The Riddler's False Notion (2) - S1-E32
Visible crew/equipment: When Commissioner Gordon apologizes to Batman, the Caped Crusader tells Gordon to be careful from whom he accepts free lemonade, and during this conversation the reflection of the boom pole/mic is visible on the Batmobile's windshield. (00:03:40)
The Pharaoh's in a Rut (2) - S1-E28
Visible crew/equipment: After Tut's henchmen carry "Bruce" from the mansion, Robin tells Alfred to meet him in the Batcave, and as Alfred walks toward the foyer a crew member is visible past the doorway, at the left. (00:11:30)
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)
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)
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)
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)
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