The Penguin's a Jinx (2) - S1-E4
Continuity mistake: Batman sends Swoop into the wall with an "OOOOFF!" onomatopoeia. The impact knocks down from the shelf a bunch of umbrellas that fall on the poor guy, but as the scene goes on, the floor is clean and the umbrellas are still on the wall rack. (00:21:30)
Continuity mistake: During the climactic fight, Batman tosses the Joker utility belt, causing confetti and streamers to fall down all over the place in some shots, while there is no such paper rain in others. (00:21:40)
Revealing mistake: The newsreel shows several issues of the imaginary Gotham City Times. Nice job with the headlines and the page layout, but every single one of them is issue number 11. (00:14:00)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: When Batman opens his drawer full of electronic (not to mention, literal) bugs, the various pseudo-creatures are arranged in different ways between the wider angles and the close-up. (00:20:50)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: When the umbrella fight erupts, the red suitcase with the money changes position on the corner of the counter (basically rotating of 90°). (00:21:20)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: The tiny spider microphone rests on the back of Robin's right hand, but the close-up shows a gloved left fist. (00:20:55)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: Adam West's hands inside the net are in a different position when Penguin sprays him with the red gas. (00:22:20)
Continuity mistake: In the cliffhanger, Riddler is putting a vice around Robin's head and cranks it; in the close-ups he turns the mechanism between his fingers, while in the shot from behind Robin's head he is turning a little handle. The height the vice is placed at is also different. (00:24:20)
Smack in the Middle (2) - S1-E2
Continuity mistake: Batman, after losing his breather between an "Urkkk!" and a "Zok!" chases down a goon that is making a run for it going for the window. Two other minions are following Batman, but their motion repeats in the next shot, when it's "Zzzzzwap!" time. (00:22:00)
Continuity mistake: The Moldavian host calls attention on the national treasure before the cake is brought. In the wide shot, just before the cut you can spot the man in white uniform turning his head to his right. In the next shot he is turning towards his left. (00:01:05)
Revealing mistake: Riddler laughing maniacally after handing Batman the lawsuit turns around and leaves, not before tipping a vase over. There is a crashing noise as if the vase shattered, but the vase is tumbling in a full 360°, undamaged. (00:11:50)
Smack in the Middle (2) - S1-E2
Continuity mistake: Elephant-man Riddler is the one man left standing in the room. The problem is, he is standing with one hand on his hip, which becomes a totally different pose at the cut, with the arm chest-high and his finger pointing down. (00:19:55)
Continuity mistake: The cake exploded and the ambassador is on the floor, his back to the tent. In the wide angle shots and in the close-up, the position is quite different; just look at the golden filigree draped over the tent. (00:01:30)
Smack in the Middle (2) - S1-E2
Continuity mistake: During the bait pursuit, Riddler tells Molly-Robin to hold the wheel for him as he puts his helmet on. The Batmobile in pursuit is featured in recycled footage, since both Batman and Robin are in it. (00:08:10)
Smack in the Middle (2) - S1-E2
Factual error: Nitrous oxide is not flammable. Not to mention, if it were, Riddler would have risked blowing everything up when he shot the gun in the room saturated with it just to give his henchmen the signal.
Smack in the Middle (2) - S1-E2
Continuity mistake: Riddler stares at Batman and Robin popping out of the stuffed animal; in the wide shot he has a (delayed, really) reaction opening up his hand, which becomes a closed fist in the next angle. (00:20:50)
Smack in the Middle (2) - S1-E2
Continuity mistake: The Prime Minister is talking about the stuffing of the mammoth; in the wide shot a couple is approaching, turning round the beast. In the closer angle, they are already behind him. (00:17:10)
Smack in the Middle (2) - S1-E2
Continuity mistake: After wu-xia style jump on the Batmobile reactor, Batman tells the girl "Wait, Molly." In the close-up there's no rope, but before and after there's still the batarang rope visible by him. (00:11:35)
Smack in the Middle (2) - S1-E2
Continuity mistake: Riddler just sent Molly to make the mask. As he sprays Robin, the strap across his chest is fastened in a different way in the close-up. (00:03:20)
Smack in the Middle (2) - S1-E2
Continuity mistake: When Riddler emerges from the ventilation system, the grate is placed against the hole. In the rest of the scene it disappears. (00:18:50)
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