The Zodiac Crimes (1) - S2-E37
Revealing mistake: After Joker's goons kidnap Crustash, the opera singer, Penguin tries to sneak off, and when Batman and Robin use javelins to capture Penguin, the glistening stunt wire attached to the javelin is visible in the wide shot. (00:18:15)
The Puzzles Are Coming (1) - S2-E31
Revealing mistake: While The Puzzler and his baddies are at Artemus Knab's penthouse, across the street from Commissioner Gordon's office, when Puzzler decides he will launch the plane himself, the wire attached to the top of the plane is visible. (00:01:15)
The Puzzles Are Coming (1) - S2-E31
Revealing mistake: At the old balloon factory, when Puzzler throws the model airplane with a poison tip at Batman, on his upper arm we can see the protruding outline of the rectangular base to which the small airplane is attached. (00:22:00)
The Puzzles Are Coming (1) - S2-E31
Visible crew/equipment: At the Knab Aircraft hangar Puzzler arrives in the truck just as Knab is leaving, and when Puzzler walks to the back of the truck the reflection of the boom mic is visible on the right back door windows. (00:14:45)
The Joker's Provokers (2) - S2-E22
Continuity mistake: While Joker and his baddies are in the vent shaft at the waterworks, Joker takes out the envelope and holds the envelope with his left palm up, but in the closeup his left palm is down as he pours the pills into his right hand. (00:14:50)
Tut's Case is Shut (2) - S2-E8
Revealing mistake: While Chief O'Hara is outside on the ledge of the top floor, King Tut commands him to use the flagpole to do acrobatics. When O'Hara obeys Tut, the vertical wire at the end of the flagpole is visible. (00:08:20)
Walk the Straight and Narrow (2) - S2-E2
Visible crew/equipment: After Archer and his goons have hit the armored truck, when the security guard pulls out the bag of money from the back of the truck and shows it to his partner, the chalk T-mark is visible on the ground between their feet. (00:10:20)
Walk the Straight and Narrow (2) - S2-E2
Revealing mistake: When the armored truck with the ten million is hit, during this scene we can see stunt wires for some of the arrows used by Archer and his goons. (00:09:00)
Walk the Straight and Narrow (2) - S2-E2
Revealing mistake: At the start, while Archer and his goons are riding toward Batman and Robin who are tied to the stakes, when the Dynamic Duo use their Bat-springs the stunt wires lifting them are visible. (00:03:05)
Shoot a Crooked Arrow (1) - S2-E1
Revealing mistake: In Commissioner Gordon's office, just as Gordon tells Dale that with Batman and Robin on their side no harm will befall the money, the top of the set is visible at the top right corner of the screen. (00:06:25)
Shoot a Crooked Arrow (1) - S2-E1
Revealing mistake: At Archer's underground hideout, Batman and Robin are strung up by their thumbs, but in fact the stunt wires that lead to their cloaked backs are visible. (00:21:40)
It's the Way You Play the Game (2) - S2-E26
Visible crew/equipment: When Batman and Robin visit Laughing Leo's Used Car Lot, the side of the Batmobile reflects a whole row of big square studio lighting panels. (00:06:30)
Marsha's Scheme of Diamonds (2) - S2-E24
Continuity mistake: In part 1, Marsha's prisoners included the mayor. Here, Batman rescues Robin, Gordon and O'Hara - but the mayor has disappeared. And oddly, no one mentions his ever having been there. (00:05:05)
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)
The Clock King's Crazy Crimes (1) - S2-E11
Continuity mistake: Clock King renders the art gallery patrons unconscious with a high-frequency sound wave. As they fall, one of the men drops his hat. When they come to and get up, the hat has disappeared. (00:15:20 - 00:19:10)
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)
The Bat's Kow Tow (2) - S2-E30
Factual error: Batman ingeniously deduces that the sympathetic vibration needed to escape Catwoman's sound-trap is the note F-sharp above high-C. What he proceeds to hum, however, is a D, and Robin hums an E. Neither of them reaches F-sharp, but the sound chamber dutifully explodes and frees them anyway. (00:02:30)
It's the Way You Play the Game (2) - S2-E26
Visible crew/equipment: The Batmobile has just pulled away, and as Andy waves good-bye, the camera shadow can be seen moving rapidly offscreen at the lower lefthand corner of the frame. (00:04:25)
The Yegg Foes in Gotham (2) - S2-E14
Continuity mistake: Just before Bruce Wayne tosses the grape to set it off, Egghead's miniature radar bomb moves to a different position on the floor all by itself. (00:04:00 - 00:05:20)
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)
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