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)
Shoot a Crooked Arrow (1) - S2-E1
Continuity mistake: The arrow Archer fires into the window frame in Commissioner Gordon's office is, depending on the camera shot, angled up, then down, up, down and up again. (00:07:30)
Shoot a Crooked Arrow (1) - S2-E1
Continuity mistake: When Batman and Robin are ensnared by Archer's net, Batman says he will get his batknife to free them. When Archer shoots them down with the arrow, they are apparently unconscious but with no explanation of what knocked them out while stuck in the net.
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: Between takes at the end of the final fight scene, most of the chairs shift positions around the table, the wooden partition screen that fell over during the scuffle has somehow folded itself, and a white cloth that was draped over one of the chairs has disappeared. (00:22:00)
Continuity mistake: At the end, when Minstrel is cornered by the Dynamic Duo, he pulls out his sparking remote unit. After being told it won't work, as O'Hara cuffs him, the unit that was in his hand disappears.
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)
Continuity mistake: Tut's crocodiles are menacing in the close-up, but in the scene where Robin is over the moving ledge, the crocodiles are very fake.
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)
Continuity mistake: When Batman is strapped into the electric chair, his utility belt is the standard flat-front, blank, yellow boxes. Once Batman breaks the wire loose to send a message, there is a large, black and yellow button attached to the the right front of the belt.
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 Clock King's Crazy Crimes (1) - S2-E11
Continuity mistake: When Clock King steals his favorite painting from the gallery, as he places it through the wall hole note the strips of tape adhered to the paintings back, and its hanging wire near the bottom (it's upside down). In the next shot from the other side of the wall hole, the painting is now turned the opposite way (it's right side up), note the tape strips. (00:16:25)
The Clock King's Crazy Crimes (1) - S2-E11
Continuity mistake: During the fight in the art gallery, the papers on the desk to the left of the screen are scattered. But in some shots of the fight progressing, the same papers have straightened themselves back into nice, neat stacks again. (00:17:00)
The Clock King's Crazy Crimes (1) - S2-E11
Continuity mistake: After starting the sand in the giant hourglass, Clock King puts on his alarm clock top hat. Between distance and close shots, the clock reads a few minutes to three, then Three o'clock in the closeups.
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)
The Clock King Gets Crowned (2) - S2-E12
Continuity mistake: Batman tosses a large white box at one of the henchmen. The box lands on the round dais of the clockworks, but as that dais begins to rotate, the box disappears. It pops back up a few shots later, now sitting on the stationary corner of the clockwork platform. But as the fight rages on, it vanishes again between shots. (00:21:30 - 00:22:10)
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)
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: 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)
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