Penguin Is a Girl's Best Friend (1) - S2-E42
Visible crew/equipment: While Batman and Robin are at the studio, Harriet and the others from the Gotham City League of Film Decency confront Penguin about scene 12. When Harriet says, "This scene is bursting with other things as well," there's a shot facing Marsha with two other women, and we can see a curved chalk mark at Marsha's feet and a chalk T-mark at the other woman's feet. (00:13:20)
Penguin Sets a Trend (2) - S2-E43
Visible crew/equipment: The Batmobile, responding to Batman's remote control activator, is supposedly driving itself through Gotham City's streets. But in one shot, even though he's crouching down, you can see the head of the film crew member actually driving the car. (00:03:00)
Penguin Sets a Trend (2) - S2-E43
Continuity mistake: Penguin's van races by a Gotham City movie theater, passing three cars parked in front of it. In the very next shot, the Batmobile zips past the same spot in hot pursuit - and there are now four cars parked there. (00:20:20)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: While Penguin and his bumpkins are hiding out in Aunt Hilda's cave, Hilda tells darling Pengy he's lucky that she's soft hearted, and the two curved chalk marks are visible on the floor where Marsha and Penguin will stand. (00:03:45)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: At the sub-treasury, when the guards hear the sound of Marsha's music they turn towards her distraction then move closer, and curved white chalk marks are visible on the floor where the actors will stand, in this shot and a following shot. (00:07:20)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: When the Dynamic Duo follow the lizard trail and go down into the manhole they end up in Hilda's cave, and when they approach Penguin's goon standing by a door, there are two chalk T-marks on the floor near that door. (00:08:50)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: When Marsha is down to one veil she ends her dance, then as she and Aunt Hilda try to get away they're stopped by the love-sick sub-treasury guards, and there's a curved white chalk mark on the floor where Marsha stands. (00:12:05)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: While Penguin and all his goons are holed up in the sub-treasury vault, in the shots of Batman, Robin, Gordon, and O'Hara waiting for three days, assorted chalk marks are visible on the floor where some of the actors stand or will stand. (00:17:10)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: As O'Hara goes to move his patrol car, the boom mic and lighting equipment is reflected on the windows.
Batman's Anniversary (1) - S2-E45
Continuity mistake: Sitting at the banquet table, Batman has placed his left hand over his chest. When the shot cuts, his hands are instantly both down at his sides. (00:05:00)
A Riddling Controversy (2) - S2-E46
Continuity mistake: When Riddler and his baddies are at their factory hideout watching the news of their criminal coup on TV, in shots facing the TV the two rabbit ear antenna are fully retracted, but in shots from behind the TV the antenna are extended by approximately a foot. Later, there's a similar occurrence with the TV antenna, while Batman and Robin use the Batrope to climb the wall. (00:03:20)
A Riddling Controversy (2) - S2-E46
Continuity mistake: At the end, Riddler's moll Anna Gram's earrings disappear, just as Batman and Robin arrive before the fight.
A Riddling Controversy (2) - S2-E46
Visible crew/equipment: During the "Batfight" at the end, it is extremely obvious that the Riddler is a stuntman and not John Astin, note that the stuntman does not have a mustache.
A Riddling Controversy (2) - S2-E46
Continuity mistake: In the park at the statue base, Batman uses a knife to open the telegram. As he reads, the knife is pointed up, and a moment later, it's down.
A Riddling Controversy (2) - S2-E46
Revealing mistake: When Batman and Robin use their jets to get out of the quicksand, as they fly up, you can see the wires used to pull them up.
The Joker's Last Laugh (1) - S2-E47
Revealing mistake: The counterfeit 100 dollar bills that Gordon and O'Hara say look "so authentic" don't actually resemble any known U.S. currency at all. In fact, a close look reveals them to be very bad photocopies of Mexican 100 peso notes. (00:01:00)
Catwoman Goes to College (1) - S2-E49
Revealing mistake: The crowd scenes during what is supposedly a Gotham City University student protest rally are inserts of rather blurry old stock footage. Not only is the mob far too large for a mere college rally, the footage is in black & white, while the rest of Batman is in color. Bit of a dead giveaway. (00:23:00)
Catwoman Goes to College (1) - S2-E49
Continuity mistake: When they first go to the bat poles, Bruce is on the right. The next shot at the bottom, Bruce/Batman is on the left and Dick/Robin is on the left. They switched sides. It has happened throughout the series.
Batman Displays His Knowledge (2) - S2-E50
Continuity mistake: When Batman and Robin are trying to escape from the giant coffee cup at the beginning of this episode, spots of moisture keep appearing and disappearing on Batman's costume.
Batman's Satisfaction (2) - S2-E52
Continuity mistake: Britt Reid visits Bruce Wayne, and while sitting on the couch, stretches forward and places both hands on his knees. But in the next take, he's abruptly leaning back with his arms folded. (00:09:30)
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