Continuity mistake: In the last couple of cuts preceding Arthur's gun accident in front of the kids, the nurse's hands are not where they should be at the cut; her hands are on the kid' shoulders, then ears, before the cut she raises them to dance on the spot, but they are back on his shoulders in the next shot. The baby patient himself when Arthur drops the gun suddenly has his hands up under the chin. (00:28:25)
Continuity mistake: In the first shot of the pediatric ward you can see on the left aisle a plush ladybug toy. When Arthur drops the gun, the toy suddenly between cuts is found in the arms of a patient, and then on the bed by him. (00:28:30)
Continuity mistake: In a close-up, Arthur grabs with both hands the gun he dropped and kicked across the hospital floor, but in the wider shot that follows he's using only the left hand, and it's also clear that Joaquin Phoenix's body is turned in a complete different way, with his feet adjoined instead of the open legs seen before. (00:28:35)
Continuity mistake: One of the Wall Street Three begins approaching Arthur, and doing so he grabs the vertical support and spins around it. There's a cut mid-spin and his buddy in the background is standing in different positions; first he is laughing leaning against the support closer to him, then he is in the middle of the subway car holding two poles. (00:31:20)
Continuity mistake: Arthur tries to get up from his seat, but one of the yuppie bullies restrains him. Then the lights flicker for a moment, but it's an editing trick, as something else changed in the car; the chips' paper bag that was sitting on one of the seats in the row facing Arthur's, is suddenly gone. It comes back right after, when Arthur is struck down by the punch, and it keeps coming and going. For instance; Joker shoots the second guy dead? Bag's on the seat. Third guy runs away? Bag gone. (00:32:05)
Continuity mistake: When one of the Wall Street Three charges the punch to hit the not-yet-Joker, his buddy in the background holds Arthur's bag with the hand on top, to the point that right before the cut his thumb sinks in the bag making it bend. When the punch lands, he's holding the bag by the side. (00:32:15)
Continuity mistake: The last of the Wall Street Three is shot as he tries to flee; he falls down in two very different takes. In the side view he choreographically falls with the jacket rolling up his back, and with the left leg (initially) forward, foot on the ground. In the previous view, camera behind Joaquin Phoenix, he fell with the sole of that foot kicked back, and with the jacket still down his back. (00:32:25)
Continuity mistake: Arthur finishes the last yuppie off, and he lies stone cold dead on the stairs. However, he is not lying in the same position the two times it is seen. The second time he has his left hand one step lower than the right (which was the only one visible earlier) and his knees are on the platform (in the first shot, only the tip of the shoes touch the floor). (00:33:45)
Continuity mistake: Thomas Wayne is speaking on TV. Arthur shushes his mom. In the close-up that follows, suddenly there's an extra lock of hair against his forehead. (00:38:50)
Continuity mistake: Arthur gets on stage at the improv club and has one of his laughing fits. When the camera is behind him, facing the blinding stage lights, you can see that he is choking himself with the right arm and holding the book with the left. But it was the exact opposite in the previous shot. (00:43:44)
Factual error: When Joaquin Phoenix and Zazie Beetz are taking a walk after Arthur's performance, between the arcade and the newsstand there's a modern video intercom with keypad, not quite fitting the 1981 setting, since the first model of its kind was introduced in 1984 (kinda odd to leave something like this in when they went through the trouble of placing appropriate arcade posters really close by). (00:45:25)
Continuity mistake: After the gig at the comedy club, Arthur and the neighbour Sophie pass in front of a newsstand. The copy of the Examiner saying "Killer Clown On The Loose" is kept in place by a clothing pin placed diagonally, top right-to-bottom left. In the close-up when Arthur looks at it, the pin is top left-to-bottom right. (00:45:25)
Plot hole: Arthur's appearance on the talk show makes hardly any sense. The show is a close port of Johnny Carson's Tonight show, for a huge audience, and yet he receives no screening at all, they put him (someone NOBODY in the staff knows the first thing about) on the air literally without a clue of what he is gonna do or say, and wearing a highly controversial costume. And, when he murders Murray, it is implied that everyone was able to see him doing that right away and he is cut 'off the air' at some point, as if the show were really live, which is preposterous for this sort of program outside of specific events (similar to how in contemporary TV "Jimmy Kimmel Live!", is not live). Even earlier when Arthur opened the letter his mom addressed to Wayne, you could hear the end credits of "Live with Murray Franklin" with the announcer saying the show is "Taped live in front of a studio audience." (00:48:00)
Continuity mistake: The camera pans towards Arthur when is reading Penny's letter to Thomas Wayne; the items on the table (newspaper, pen) are in a different position compared to the rest of the scene. (00:48:35)
Continuity mistake: When Arthur is choking Alfred Pennyworth through the bars, in the shot when he says "Let go, let go!" you can see behind his head the flowers from the magic wand, absent in the previous views. (00:54:50)
Other mistake: Arthur watches Murray's show in the hospital room, he is able to see himself in the Pogo's Comedy Club performance. Forgetting how very contemporary this whole "viral video of person making a fool out of himself" dynamic is, and how astronomically unlikely it is that there would be taping of some open mike session in a club, it still makes in fact sense that there could be a recording of Arthur's performance, since there is a monitor backstage and in an earlier scene there was a guy with a camera on a tripod far in the back of the room when Arthur was taking notes. But in the video shown during Murray's opening there are 2 different angles of the performance, which are also different from the one show in the monitor backstage. Amateur night with 3 cameramen and a director/editor? Come on. (00:59:50)
Continuity mistake: In the theater lavatory, Arthur puts the usher jacket in the sink. Part of the jacket drapes to the side of the sink, but at the cut the cloth is entirely contained in it. (01:05:00)
Continuity mistake: After Arthur took off the stolen jacket and hat when talking to Wayne he places them in the sink, but in the next cut they disappear. (01:05:00)
Suggested correction: You don't see the sink containing the clothes anymore after he puts them down.
Continuity mistake: Thomas Wayne and Arthur Fleck are talking in the bathroom. Joaquin Phoenix's hair changes position on his forehead several times even when he does not touch it and/or shakes his head. (01:06:15)
Continuity mistake: After Arthur steals the file from the guy in Arkham he runs and the file moves from one arm to the other. (01:13:10)
Suggested correction: I don't see this is a problem due to the fact that we can't be sure what really happens as apposed to what only happens in Arthur's mind. So if the whole TV show appearance is just another fantasy, he would have skipped the who screening process.
You are free to treat the whole movie as something where things don't make sense because in the fan theory of your liking it's all meant to have subtle hints that the movie is all a fantasy, but the movie does not present that particular talk show scene as a dream sequence. It'd be silly to nitpick the logic in the scene when he is picked from the audience by Murray at the beginning because it's obviously presented as nothing more than his fantasy, but his appearance on the show is what the movie built up to up to that point and is not treated as a parenthesis where logic should be suspended, nor disproven like the scenes with his girlfriend standing in.
Sammo ★
Suggested correction: The points raised are logical in the context of our real world. However, in the film world, different rules/logic can apply, and apparently do. In the movie world, this show is live, etc. Saying that something is taped live doesn't mean that it isn't also broadcast live; the two don't have to be mutually exclusive. They could just be saying that so people don't think they use a laughter track.