The Penguin's a Jinx (2) - S1-E4
Other mistake: In the pre-credits recap of part 1 of the episode we see Bruce awake and staring in horror (with actually a super hilarious face) at the furnace. It was not part of the previous episode at all and in fact Bruce wakes up only in this second episode.
Continuity mistake: The Joker sends a doll crashing through the window of Commissioner Gordon's office. O'Hara is holding in close-up the doll in a different way from the wider shots, and the jester cap of the figurine is also blatantly folded in a different fashion. (00:18:30)
The Penguin's a Jinx (2) - S1-E4
Other mistake: Penguin is able to follow from his office the unconscious Bruce Wayne on the conveyor belt. Considering the angle and how it keeps perfect close-ups of the moving target, it would mean he has a security camera in the back of his shop that is pointed on the conveyor belt and is mounted on a dolly (and he is not doing anything to control it). Definitely wins him Evil Overlord points. (00:02:40)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: When Penguin pulls the lever, Adam West assumes the position to receive the net dropped on his head a couple of seconds early and as if Bruce/Batman knew beforehand that something was coming from the ceiling, in that spot, passively accepting it. (00:22:10)
Smack in the Middle (2) - S1-E2
Continuity mistake: After the Garbo joke, the various extras begin to pass out from the gas with multiple inconsistencies between shots. In the shot that follows the joke, the woman with the red and black dress is fainting, but she's back up in the next, in which the policeman goes down, only to be up in the one later, etc. (00:19:35)
Smack in the Middle (2) - S1-E2
Revealing mistake: Batman tosses the Batarang at Riddler after bursting through the door and yelling "Surrender, you rat." Such is Adam West's physical prowess and the strength he puts in the athletic gesture, that the mere touch of his foot moves the heavy cement block lying on the floor. That or it's made of plastic (same one he picks up later in the scene tossing it at the 'bulletproof glass'). (00:14:30)
Smack in the Middle (2) - S1-E2
Continuity mistake: Riddler wakes Robin up, and the Boy Wonder does not waste time in his tongue lashing. During the scene, the lighting on set is very noticeably different; with the camera positioned between the two, Frank Gorshin's jaw casts a shadow; with the camera behind Burt Ward, it's him casting a big shadow on the green unitard. (00:03:40)
Other mistake: At the end of the episode when the cattle are stampeding, the sign over the Saloon is backwards.
Revealing mistake: To free himself from the Joker's goons, Batman throws a gas capsule on the floor. Two things; first, the Joker is instantly asphyxiated by a lot of smoke, but when the henchmen let Batman go in the next shot, the puff of colored fumes has barely started to rise, and the Joker is further away. Second, the capsule that Adam West throws with panache on the ground and that should generate the noxious cloud can be seen actually bouncing back up after his energetic toss. (00:15:30)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: At the beginning of the big fight with Penguin, everyone is doing some fencing with the umbrellas. The guy with the caveman face on the left switches stance depending on the camera angle; he's lunging forward waving his umbrella with one arm in the frontal views, and he's in a guarded position in the overhead shots. (00:21:20)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: In the close-ups of the basket filled with umbrellas at the bank, the asbestos blanket is continuously bumping up and shaken not by the 'explosions' of the booby trapped parasols, but rather by the thin wires you can make out at the top of the frame. (00:15:10)
Fine Feathered Finks (1) - S1-E3
Revealing mistake: The trademark vertical rope climb of this episode is done on the handle of a huge umbrella. The umbrella though is at an angle in the various wide shots, and Batman is climbing a perfectly vertical handle. (00:18:30)
Continuity mistake: Arriving at the museum, the dynamic duo is greeted by some rabid Robin fans; when they start screaming and cheering for him in a close-up, there are men passing by behind them that were not there in the wider shot with the Batmobile approaching. (00:09:40)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: Robin jumps on a table, dodges a swing and gives a (really weak) kick to his adversary. Cut, and he is nearly tripping over two umbrellas on the table he is standing on, suddenly appeared out of nowhere. (00:21:40)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: The bat-phone rang, and Dick is practicing his French. Bruce in the wide shot has taken his pen off the sheet, but he is in a different position in the close-up that follows. Same when he mentions the "key to world peace"; his hand changes position. (00:03:25)
Continuity mistake: When Joker shows off for the first time his utility belt, it switches sides between shots. First each pocket has its buckle on the right, towards the blonde bimbo, then in close-up the buckles are on the left, and when it switches back to a wider angle, again they are on the right. (00:16:45)
Smack in the Middle (2) - S1-E2
Continuity mistake: Riddler sedates again Robin with the "B" spray. He puts his own mask back on, and on the table the spray can is turned with the letter facing away from the camera. Riddler takes a peek at the unconscious Robin, and in the next shot both sprays have their letters properly showing, only to be hidden again when the same camera angle as before is used again. (00:05:55)
Fine Feathered Finks (1) - S1-E3
Continuity mistake: The dynamic duo enters the umbrella factory and begins talking with the Penguin. Right away you can see the cigarette in the holder has its tip turned into ash, but in the close-up on Burgess Meredith's grin a greater part of the cigarette is consumed. (00:16:40)
Smack in the Middle (2) - S1-E2
Revealing mistake: Of all the possible mistakes related to the Robin mask Molly supposedly wears, the one that really could have been avoided was the fact that the camera does not cut away from Burt Ward while he is in the middle of the gesture of turning around and 'ripping away the mask', but only after he's done it, so you can tell nothing came off, nothing moves in his hair, let alone the face itself. (00:10:25)
The Penguin's a Jinx (2) - S1-E4
Continuity mistake: Batman punches Hawkeye with a BAM; in the closer view Robin is not where he is supposed to be (next to the elevator, where he was sent reeling by the punch and where the action takes place in the following shot). (00:21:45)
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