Batman Stands Pat (2) - S1-E14
Continuity mistake: At the end, as Bruce Wayne speaks to Magda, he's standing with his arms at his sides. When the shot cuts, his hands are suddenly clasped in front of him. (00:23:30)
Continuity mistake: In close-up, Bruce Wayne folds his newspaper in half, leaving the folded edge facing the camera. The shot cuts to a wider view and immediately, the paper has reversed positions in his hand. (00:04:00)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: When the Penguin goes to Wayne Manor to put Batman and Robin to sleep with the gas from his umbrella, just before he shoots the orange gas at Robin's suit of armor, there's a quick shot of the armor's helmet. The problem is that there's already an orange stain on the face of the helmet from the orange gas that comes out of the tip of the umbrella, even before Penguin shoots any gas. (00:19:15)
Continuity mistake: When Batman and Robin crash through the window, there's no glass left in the frame - at least not until the next shot, when several large shards that weren't there before suddenly appear at the edges. (00:11:50)
Batman Stands Pat (2) - S1-E14
Visible crew/equipment: When Mad Hatter is sending Lisa in to butter up Mr. Bowinkle, the microphone shadow is bobbing up and down above their heads. (00:11:25)
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)
Visible crew/equipment: When Harry plots to replace Chandell, the polished grand piano behind him reflects the moving lights on some of the studio equipment. (00:15:30)
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 Joker Trumps an Ace (1) - S1-E25
Factual error: Though he's a bastion of knowledge and a member of the museum board, Bruce Wayne completely mangles Egyptian history - twice. He says that King Tut ruled in the 14th Dynasty, and that the museum's mummy was a 14th Dynasty king who ruled in 1500 BC. Wrong on both counts. Tut reigned from 1336-1349 BC. The 14th Dynasty ran from 1773-1650 BC. Wayne would have known that - and so would his well-educated colleagues, none of whom points out the error. (00:13:00 - 00:15:00)
The Zodiac Crimes (1) - S2-E37
Continuity mistake: Robin is holding an upright 8-foot pole when Venus sprinkles her knock-out glitter on the Dynamic Duo. When the shot cuts and they fall to the floor, the pole has completely disappeared. (00:22:10)
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)
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)
The Yegg Foes in Gotham (2) - S2-E14
Visible crew/equipment: During the final egg fight, the microphone shadow puts in an appearance on the wall behind the bad guys. (00:21:50)
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)

Smack in the Middle (2) - S1-E2
Continuity mistake: Just after the Joker tells the fake Robin to turn on her homing beacon, a quick shot of the Batmobile approaching shows it isn't glossy black with cherise red trim as normal, but is instead flat black with white trim. This footage was from pre-series testing, painting the car different ways to see how it would look best on film, but somehow this footage was actually used in the episode by mistake. (00:06:20)
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)
Not Yet, He Ain't (2) - S1-E22
Factual error: When the Penguin steals the Batmobile, Batman spies on him from a tiny camera he says is hidden behind the car's fuel gauge. But the picture he and Robin are viewing has been shot from several feet away from the car, not from inside it. (00:11:15)
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)
The Clock King Gets Crowned (2) - S2-E12
Factual error: Trapped in the overturned hourglass, Batman and Robin lie flat and begin furiously digging in the sand, making the hourglass roll out the door. But to cause such rapid movement, they'd need to be applying their weight against one of the glass sides (like a hamster in a ball). Just digging in the sand wouldn't get them anywhere, at least not that quickly. (00:04:15)
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