Mr. Monk Takes Manhattan - S3-E1
Continuity mistake: In the scene where the two guys are playing chess, the guy with the black hat knocks over the chess pieces after losing. He then starts scrambling up the pieces and leaving his hands near the chess board. When the shot changes to a wide shot of Monk walking away the guy suddenly has his hands on his head.
Mr. Monk Takes Manhattan - S3-E1
Continuity mistake: When Monk is lost in the street crowd after getting pushed into the subway car, his left shirt collar is sticking up over his coat. It's still up when he puts his hands to his head, but is tucked neatly back in in the next shot, though he still has both hands on his head. A few seconds later, it's the right collar flap that's sticking out instead.
Mr. Monk Takes Manhattan - S3-E1
Factual error: The .22 caliber shots would be a higher pitch.
Mr. Monk Takes Manhattan - S3-E1
Factual error: In the episode the victims were murdered with a .22 caliber firearm. However, a short shot of the crime scene focuses on an empty shell casing which comes from a larger caliber firearm, most likely a 9mm parabellum. (00:05:30)

Mr. Monk Takes Manhattan - S3-E1
Continuity mistake: The angle of one of the victims' heads visibly changes from shot to shot while Monk is investigating the scene. (00:05:30 - 00:06:25)
Mr. Monk Takes Manhattan - S3-E1
Continuity mistake: There is a shot where Randy is trying to cross the police tape and an officer stops him, and he can be seen briefly arguing. However, when it cuts to the next shot, we see that argument happening again in the background, repeated. (00:07:20)
Mr. Monk Takes Manhattan - S3-E1
Audio problem: The captain can be seen speaking, but no audio of him is heard. (00:14:10)
Mr. Monk Takes Manhattan - S3-E1
Revealing mistake: Monk's reaction to the gunshots begins just before the gunshots go off. (00:03:55)
Answer: The two men are trying to work out a secret deal between them without involving the union, which means the workers' interests aren't being represented and defeats the whole purpose of a union. The mayor would lose labor's support and Cusack's union troubles would just be starting.
Captain Defenestrator