Continuity mistake: In the scene in a bar where Costello talks to the young Colin Sullivan, the time in his watch is evidently very different in two shots (when he takes the money from the bar owner and later when he hands Sullivan a bunch of coins). First it reads 2:50, then 2:58, and only one and a half minute has passed in the movie, as shown by Costello talking. Also, the watch in the second shot has no seconds hand, only hours and minutes. (00:03:20)
Factual error: When Costigan is riding the "T" (Boston subway), he is talking to Queenan on a cell phone. However, they are on the "Red" line, which is obvious because of the red walls in the tunnel. Cell phones don't work on the Red line because it is underground and there are no cell phone routers in those tunnels.
Continuity mistake: In the final scene of the movie, when Sullivan is walking down the hallway and into his apartment, his belt is light brown. But when he's dead on the floor, it's a dark brown, almost black.
Continuity mistake: At the very last shot of the movie, taken from inside Sullivan's apartment, the Massachusetts State House appears to be quite closer than in other shots from the apartment - e.g. when Sullivan first rents it.