Surf's Up! Joker's Under! - S3-E10
Visible crew/equipment: After Batman wins the competition, when Hot Dog is finally released from the trash can Joker rushes over to claim it was just a little joke, and the microphone pops up into view at the bottom of the screen. (00:21:10)
Marsha, Queen of Diamonds (1) - S2-E23
Continuity mistake: After Batman has been hit by Marsha's love dart, when Robin pulls the dart out and then begs Batman to resist it, in these semi closeups note Burt Ward's uncovered forearm with his still-healing burn wound. Then, while the Dynamic Duo fight Marsha's sabre wielding goons, Marsha hits Robin with another one of her darts and orders him to attack Batman. When this happens, Burt Ward's forearm now has a compression bandage around the wound. (00:13:55)
I'll Be a Mummy's Uncle - S3-E23
Visible crew/equipment: When King Tut runs back up the shaft and encounters Batgirl, Commissioner Gordon, and Chief O'Hara, he is reveling giddily in the truth he has discovered. Then, when Batman and Robin show up, their chalk T-marks are visible on the ground. (00:21:10)
The Zodiac Crimes (1) - S2-E37
Visible crew/equipment: After Joker has stolen the map from Commissioner Gordon's office, he rushes to the window and calls for Venus, then just as Joker places his foot onto the lowest ladder rung, we can see a crew member's hand holding the same rung near Joker's foot, at the bottom of the screen. (00:02:05)
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)
It's the Way You Play the Game (2) - S2-E26
Visible crew/equipment: At the Batcave, when Batman and Robin use the Batroscope it leads them to the Adobe Hacienda Motel and Eats, which serves the best chili and avocado dip in GC. When it cuts to them entering the building, at the start of this shot the shadow of the moving boom mic is visible in the bottom right corner of the screen. (00:09:30)
Scat, Darn Catwoman (2) - S2-E41
Visible crew/equipment: While Batman and Catwoman are at the Batcave the alarm goes off, so Batman activates the Diversionary Batphone Lines gadget, then it cuts to Pat Pending counting his cash, and when Commissioner Gordon and Chief O'Hara storm in, two chalk T-marks are visible on the floor near the bed. (00:12:30)
Visible crew/equipment: After Batman and Robin use their infrared eyeglasses on the Parker boys, Batman turns on the emergency generator switch and Legs escapes. Then the Dynamic Duo deliver a bit of exposition, and when they walk over to Ma Parker, their curved chalk marks are visible on the floor behind Robin. (00:22:10)
The Penguin Declines (3) - S2-E39
Visible crew/equipment: When Venus is at the Batcave, loads of fisticuffs ensue between the Caped Crusaders, Joker, Penguin and all the baddies. While Robin is up on the atomic pile scaffolding he punches one goon off the ladder, then as he falls we can see the edge of the brown crash mat rise up, right before the word "SPLATT!" appears onscreen. (00:20:50)
Visible crew/equipment: When Olga shouts, "Da, da, da! Drowning her in caviar!" in the overhead shot, the boom mic repeatedly dips into view over Olga, at the top of the screen. (00:21:55)
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)
The Penguin Declines (3) - S2-E39
Continuity mistake: When Joker's goons return from Operation Laundry Bag and finally release Penguin from the bag, Penguin's hat is secured on his head with an elastic strap, but this strap vanishes in the next shot. (00:04:30)
The Penguin Declines (3) - S2-E39
Visible crew/equipment: When Batman and Robin bring Venus to the Batcave, just as she says, "It's fabulous," the reflection of the moving boom pole/mic is visible on one of the Bat-computer screens, at the bottom right corner of the screen. As this shot continues, when Robin points out their Bat-radar, a chalk T-mark is visible on the floor near Batman's foot. Then, when Penguin, Joker, and the goons appear, more chalk T-marks are visible on their side of the floor. (00:17:10)
The Yegg Foes in Gotham (2) - S2-E14
Visible crew/equipment: After Bruce defeats the radar egg using a grape it cuts to Commissioner Gordon at the raccoon pellet ceremony, and when the millionaires walk in, there are two chalk T-marks visible on the floor, beside Chief Screaming Chicken.
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)
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