Fine Feathered Finks (1) - S1-E3
Revealing mistake: After the huge rooftop umbrella is launched onto the street there's a small umbrella hanging from its handle, and when Batman uses his Batarang to swing towards the huge umbrella's shaft, his stunt wires are visible. (00:18:45)
Fine Feathered Finks (1) - S1-E3
Visible crew/equipment: In Commissioner Gordon's office, when Gordon is looking over the paperwork of three new umbrella factories, frustrated that none are in the name of Penguin, as he stands up we see two white tape marks on the rug behind him. In the previous scene with Warden Crichton, four of the actors had been standing in that area. (00:11:35)
Continuity mistake: When Robin has the idea that Riddler placed two other riddles hidden in the legal documents, Robin holds the papers up with his raised right hand, but in the next shot the documents are being held up in Robin's left hand. (00:13:45)
Continuity mistake: At the secret HQ of the Mole Hill Mob, Molly is wearing a ring on her right hand and many bangle bracelets as she dances, but in the closeup when reaches into the caviar jar the ring and bracelets are gone, then it all reappears. (00:15:00)
Revealing mistake: At the start, when Joker has sprung himself from prison, there are three shots of the giant spring, and the wires holding up the platform at the top are visible. In the third shot, one of the wires even glistens for a moment as it moves. (00:02:35)
Death in Slow Motion (1) - S1-E31
Audio problem: In the distance shot, when Robin responds to Batman's call, his lips don't move, but you hear him.
Not Yet, He Ain't (2) - S1-E22
Continuity mistake: When the Batmobile is blocked by the second police car, it's stopped on an angle, and almost touching the car. When the Penguin commandeers the Batmobile, it's sitting correctly on the road, so that it can be driven easily without really needing to back up.
Other mistake: When Mr. Freeze is moving through the room evaluating the diamonds, the tanks on his back can be fire extinguishers. There is no way that the "weapon" attached by hose to them will work, as the handles have to be squeezed to discharge.
The Joker Goes to School (1) - S1-E15
Audio problem: As Susie deposits a dime in the coffee machine, the camera starts to pan down towards the opening where the cup will appear. You hear the cup then the quarters fall, but you can see the cup full of quarters is already in place before the sound is made.
The Joker Goes to School (1) - S1-E15
Continuity mistake: As Batman goes to cuff the Joker, the Joker holds up his right hand. In the close up, his left hand is raised.
The Penguin's a Jinx (2) - S1-E4
Revealing mistake: Robin deals with the Penguin henchman in the elevator, then suddenly jumps on the counter, watches Batman conk heads (in a real fake way) and starts laughing like a slightly demented person. In all that, the guy in the elevator was still standing and looking like he was waiting for his cue. He is just suddenly KO with no explanation in the full view of the room a moment later. (00:21:50)
Fine Feathered Finks (1) - S1-E3
Factual error: The show is obviously full of cartoonish hyperboles; particularly amusing the notion that the "tempering furnace" in the back of Penguin's shop reaches 10'000° (I assume Fahrenheit), which would make it hotter than the surface of the Sun and able to melt any known metal on Earth. Bit of an overkill to temper umbrella ribs. (00:24:10)
Continuity mistake: Batman and Robin are being summoned by Commissioner Gordon, but are still in civilian clothes, so it's time to get to the Bat-cave. Bruce presses the switch and the bookshelf begins to slide open. Pay attention to the white books in the third row and the red books on the top shelf. In the close-up that follows there are fewer white books, their cluster aligned with the last of the red books, a different proportion from the previous shot. The name tags on the bat-poles are also misaligned in the wider shot and perfectly at the same level in the close-up (which is a reused shot from the pilot episode). (00:05:10)
Continuity mistake: Despite his lackadaisical pitching, the Joker manages to eliminate a series of batters. In particular, there is one elimination before and after the warden tells O'Hara about the joys in life, when Joker didn't really have time to throw the ball 2 more times. (00:01:55)
Revealing mistake: Right at the end of the obligatory Bat-rope climb scene, look at Robin's cape; the wire that is used to keep it in place (aka sticking out to make it look like it is subjected to gravity and drapes down) loses position too soon, so the real gravity causes the cloth to go towards the wall the dynamic duo is supposedly walking vertically on. (00:11:30)
Other mistake: The Joker's escape is so cartoonish and ridiculous you wouldn't even know where to start; besides the fact that the explosion somehow engulfs instantly the whole baseball field, the guard on top of the wall is following his movement with the gun, so he sees the Joker, therefore the smoke screen is useless, not more effective in any way than the mere surprise of a coil suddenly springing up from the ground.
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)
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