The Minstrel's Shakedown (1) - S2-E5
Continuity mistake: When Alfred brings the lunch tray down to the Batcave, Batman is holding a soldering iron, working on the electronic bug. When the shot cuts to a close-up, the soldering iron vanishes, and he's holding a clear plastic probe instead. (00:10:15)
Continuity mistake: While Batman is telling Octavia that she can go free, his hands are either straight down at his sides or clasped together at chest level, depending on the shot. (00:06:15)
Continuity mistake: Mr. Freeze has frozen the commissioner's office, and when Batman applies plastic explosive to the door, a frost stripe appears that wasn't there in the master shot a moment before. In the next shot, the putty he's just put there disappears. And when the explosion occurs (even though Batman didn't add any detonators), it doesn't emanate from anywhere near the spot where he applied the putty. (00:06:00)
Shoot a Crooked Arrow (1) - S2-E1
Continuity mistake: When the Archer robs Wayne Manor's safe, an unconscious Dick Grayson shifts positions on the floor between takes. At first, he's lying with both hands folded over his chest. A few shots later, his left arm is stretched out over his head. (00:01:30)
The Joker Trumps an Ace (1) - S1-E25
Continuity mistake: The Joker reveals himself by throwing off his cape, which drops to the floor behind him. But when the shot cuts, the cape instantly disappears. (00:00:50)
The Puzzles Are Coming (1) - S2-E31
Continuity mistake: In the Batcave, Batman is holding Puzzler's pink balloon while he and Robin deduce its clues. The shot cuts to a wider angle when they turn to race to the Batmobile, and the balloon disappears. (00:12:50)
The Impractical Joker (1) - S2-E21
Continuity mistake: Toward the end of the fight in the fur salon, one of Joker's henchmen shifts locations instantaneously. In the first shot, he's on the far side of Robin, falling against the wall. In the very next shot, he jumps to a spot between Robin and the camera, where he takes a swing at Batman. (00:17:00)
Continuity mistake: Batman folds up the Bat Shield and starts to tuck it into his belt, which it is much too large to fit into. In the very next shot, the shield has disappeared. (00:21:00)
Continuity mistake: Tied to a conveyor belt, Batman and Robin move past a stack of boxes stenciled with the factory's name. Cut to close-up, and they're now back to a position right next to the boxes. Back to master shot, and the boxes are once again several feet away - at least until the next close-up. (00:02:50)
Continuity mistake: As Tut prepares to re-animate the scarab beetles, his apothecary henchman stands to his immediate right, close enough to touch his shoulder. But when the shot cuts to a wider angle, the man is standing a foot away. (00:08:45)
Tut's Case is Shut (2) - S2-E8
Continuity mistake: Tut's "pets," which are a little too obviously plastic, are crocodiles (with pointed snouts), and they're sitting on a grassy island in their water tank. The stock footage inserts, however, are of alligators (which have flat snouts) swimming in open water, with no island in sight. (00:02:30)
The Zodiac Crimes (1) - S2-E37
Continuity mistake: Joker's floating zap-wand is hanging in the air right in front of Chief O'Hara's face. But when the shot cuts, it's instantly ten feet away, and is now floating behind the Joker. (00:01:45)
The Clock King Gets Crowned (2) - S2-E12
Continuity mistake: Batman and Robin are trapped in the overturned hourglass. They're sitting upright when Batman suggests an escape plan. In the very next shot, they're sprawled face down on the sand. (00:04:15)
Not Yet, He Ain't (2) - S1-E22
Continuity mistake: Penguin loads all his loot into the stolen Batmobile - so much loot that the trunk can't close. Yet in the very next shot, as he drives away, the trunk has somehow shut itself. (00:17:30)
He Meets His Match, the Grisly Ghoul (2) - S1-E16
Continuity mistake: In the bistro, Batman thwarts Joker's booby-trapped juke box by whipping out his bat shield. Afterward, he places the shield on the floor behind him. In the next shot, as he turns around, the shield has disappeared. He and Robin race off without retrieving it. (00:15:00)
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)
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)
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)
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)
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