Hizzonner the Penguin (1) - S2-E17
Other mistake: When Pengy shows up at the Grand Order of Occidental Nighthawks he feigns shock, then as he shoves his umbrella into the vat of sulfuric acid, Penguin moves his arm/hand toward the right to pull out a different umbrella, one that appears destroyed by the acid. (00:22:55)
The Devil's Fingers (1) - S2-E15
Visible crew/equipment: When Commissioner Gordon calls Chandell to reassure him that Batman and Robin are back in action, Chandell shares more root beer with Harriet. Then, when he hints for her to leave, a T-mark taped to the floor is visible at the lower left side of the screen. (00:18:20)
The Penguin Declines (3) - S2-E39
Revealing mistake: At the Batcave, when Penguin is up on the atomic pile scaffolding Batman grabs hold of him just as Pengy uses his umbrella to float down, and the stunt wire attached to the umbrella ferrule is visible while the duo descend together. (00:21:05)
Visible crew/equipment: After the first couple of shots of the Batcopter, when it cuts to Mr. Freeze at his refrigerated refuge, the two black tape marks are visible on the floor near Professor Isaacson's and Glacia's feet.
Batman's Satisfaction (2) - S2-E52
Continuity mistake: While the Batcomputer starts acting wonky just as Batman and Robin need it to figure out Pinky's location, when Alfred joins Batman and Robin in the Batcave, the Yellow Pages phone book vanishes from the Batcomputer's shelf in the closeup. (00:12:20)
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)
The Catwoman Goeth (2) (a.k.a. A Stitch in Time) - S2-E34
Visible crew/equipment: While Batman stands outside the run down factory, the GC rookie officer asks, "Who's Robin?" and both GC officers get back into their patrol car. Then as they drive away the reflection of equipment (looks like the boom pole) becomes visible on the vehicle's rear passenger window. Then it cuts to Batman, and the reflection of the boom pole is visible on the Batmobile's windshield, at the bottom right corner of the screen. (00:12:25)
The Duo Is Slumming (2) - S2-E32
Visible crew/equipment: When Puzzler and his high-flying flunkies exit the shed it cuts to the Retsoor in Knab's hangar, and a few chalk T-marks become visible on the ground near the nose of the plane. (00:19:40)
Marsha's Scheme of Diamonds (2) - S2-E24
Visible crew/equipment: At GCPD, when Marsha and her Grand Mogul enter Commissioner Gordon's office bringing with them a cage with two toads, there are two white tape marks visible on the rug beside the desk. (00:19:35)
Hizzonner the Penguin (1) - S2-E17
Visible crew/equipment: At the start, when Penguin rescues a blind vendor in view of a GCPD officer, Penguin claims that the accusation he would molest a minion of the law is inconceivable, then as he pushes the vendor toward the officer, two chalk T-marks are visible on the ground. (00:00:50)
Hizzonner the Penguin (1) - S2-E17
Visible crew/equipment: After Batman and Robin are captured at GOON HQ, when it cuts to the bound Caped Crusaders hovering over a vat of sulphuric acid, in the overhead shot some chalk actors marks are visible on the floor beside the vat, at the bottom of the screen. (00:22:00)
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 Greatest Mother of Them All (1) - S2-E9
Visible crew/equipment: While the GCPD has the Parker house surrounded Ma sits herself down on a rocking chair, and in the next shot as the officer uses the bullhorn to announce she doesn't have a chance, the reflection of the boom pole/mic is visible on the windshield. (00:07:05)
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)
The Joker's Hard Times (2) - S2-E38
Continuity mistake: After Joker enters Commissioner Gordon's office, Gordon and Chief O'Hara walk over to the window, and the Batphone table is behind them, beside Gordon's desk. Then Joker makes two "quick-frozen cops" and runs off to snatch Justice, leaving Gordon and O'Hara immobile. When their shock paralysis wears off, Gordon and O'Hara rush over to Gordon's desk, but the Batphone table and the Batphone have vanished (note the rug's pattern). (00:03:00 - 00:04:55)
The Joker's Hard Times (2) - S2-E38
Visible crew/equipment: After Joker and his henchmen steal the statue, it cuts to Commissioner Gordon and Chief O'Hara as they recover from their shock paralysis, and when they walk over to Gordon's desk, the wheel of filming equipment is visible at the right side of the screen. (00:04:55)
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 Is a Girl's Best Friend (1) - S2-E42
Visible crew/equipment: When Harriet, Alfred, and the others arrive at the studio while Batman and Robin are on set, the actor's curved white chalk mark is visible on the floor where Alfred stands. (00:12:10)
Pop Goes the Joker (1) - S2-E57
Continuity mistake: After Oliver Muzzy congratulates Joker for his magnificent artwork and makes a deal with him, before Joker leaves the gallery he runs his finger across Batman's yellow emblem to sign his red artwork, but at GCPD HQ when they're discussing the matter, Joker's signature is completely different, it's now a capital "J" on Batman's yellow emblem. (00:06:45)
Caught in the Spider's Den (2) - S2-E56
Visible crew/equipment: In Commissioner Gordon's office, when Gordon and Chief O'Harah walk over to the Batphone so they can talk to Robin and get him to surrender, we can see the actor's white tape mark taped to the rug, just as Gordon removes the clear acrylic dome from the Batphone. (00:17:20)
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