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)
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: 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 ★