Continuity mistake: Murray's blue jacket, when he comes out from behind the curtain his jacket is open, than he makes a twirl and the first button of the jacket is buttoned up.
Factual error: The ambulance that crashes into the police car Joker is riding in towards the end of movie has the styling of a contemporary vehicle, not one from the early 1980s.
Audio problem: The police officers chase Arthur to the subway. When the subway train starts moving after they just barely got in, the sound resembles the acceleration sound of a R143 subway car, which actually didn't exist until 2001, but it's a much older car, the R32.
Plot hole: Given Arthur's mother was placed in an asylum it seems unlikely she would've been allowed to keep him once released. The state would've placed him in another home.
Suggested correction: Nobody says she raised him as a child. As soon as he turned 18 he could have chosen to live with her again. Quite possibly because he didn't like his foster home.
Continuity mistake: Arthur's cuffed in the police car, but he's uncuffed once laid out on the hood.
Continuity mistake: At the end when Arthur/Joker dances on the police car's hood in front of the crowd, in the shot behind him he keeps his arms down, but when it changes into a frontal shot on him he keeps them lifted up.
Continuity mistake: When Joker confesses that he was the one who killed the three guys in the subway at the Murray Franklin Show and also says "It's not a joke", he keeps his gaze turned towards Murray in one shot and towards the audience in the next.
