Continuity mistake: When Sullivan is checking the CCTV recording, we can see the "citizens" envelope, lying on his coat, on a desk or a chair. First, the folded part of the envelope with "citizens" written on it is upright, with the word appearing upside-down. Then, as he grabs his stuff to leave, the position of the envelope has changed to horizontal. (01:30:00)
Character mistake: During the funeral at the end before the 21 gun salute, the NCOIC called for "half left face", that would cause everyone to get shot in the face.
Suggested correction: Half-left face means a 45° left turn (left face is a 90° turn), so wouldn't result in anyone getting shot.
Continuity mistake: Costello throws money down on the pool table and tells Costigan to get his hand fixed. In the next shot he has the money in his hand and throws it down again.
Continuity mistake: When French is holding the bag with the hand he places a ring very close to Costello's cheek. A second later, without him having moved, the hand is at jaw level and farther away.