Continuity mistake: When Costigan is with Madolyn in her office, the tissues in the tissue box change consistently between shots.
Continuity mistake: The top layer on their dessert changes when Sullivan and Madolyn are in the restaurant. Between shots, the top piece changes back and forth between flat and curved.
Continuity mistake: When Costello and French encounter the cops, the first shot shows the cops' car turning their lights on. In a new shot a second afterwards the lights on the middle and right side cars are out and they are turning them on again. On yet another new angle, the lights on the car on the left turn from off and on again in a split second.
Continuity mistake: In the scene after Queenan dies, when Sullivan picks up his phone, the number Sullivan calls Costigan in isn't the same as the one from which Costigan calls back, even though it's the same mobile (silver and blue vs. Costigan's red phone for Costello's gang). When Sullivan calls, the number begins with something like "617-854" and when he sees Costigan calling back, it's "617-177".
Continuity mistake: While Queenan is talking to Costello out on the street, watch the people behind him. First there's no one, then we have a shot of a woman and a huge line of kids passing next to her. Then back to Costello and the woman, who hasn't moved, is now miraculously visible behind him. To add to the mess, the kids have vanished.