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)
Continuity mistake: When Frank and Francis executes the couple on the beach, the woman falls almost on top of the man's back. When it cuts her body has almost moved off him. Then in the next shot she is on top of the man again. (00:04:15)
Continuity mistake: When Jack Nicholson approaches a young Matt Damon he has a cigarette dangling from his mouth. When the camera faces Nicholson he has no cigarette. (00:04:55)
Visible crew/equipment: When Ellerby introduces Dignam and he describes his undercover unit, a microphone is seen moving around at the top, center of the screen. (00:23:10)
Revealing mistake: In the scene where Costello is smashing Billy's hand with the boot heel, you can tell from the position of Billy's arm that Costello is hitting the pool table rather than Billy's hand. He is actually hitting his own hand more than he could possibly be hitting Billy's. (00:36:00)
Other mistake: When Jimmy Bags reaches for his cigarettes, Billy's gun hits his forehead. But after the cut to French's face, Jimmy Bags is spitting up teeth. (00:43:00)
Continuity mistake: In the scene where Alec Baldwin is briefing the cops on the micro processor bust, his shirt has distinct sweat patterns. These patterns change between scenes, back to original then finally almost dry. (00:59:55)
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)
Continuity mistake: In the scene after Queenan dies, when Sullivan picks up his phone to contact Costigan, he presses the "talk" button and a smudge of blood is left. In subsequent shots, there's no trace of blood on the "talk" button. (01:49:45)
Other mistake: When Costigan drags a handcuffed Sullivan into the elevator, Costigan slams Sullivan against the wall and his left arm is visible and not in handcuffs. (02:13:05)
Continuity mistake: When Ellerby attacks the guy for not installing the cameras in the right place, he knocks off a map from the board. A second later Ellerby is still going after him, and the map is fixed.
Revealing mistake: When Costello's men drive off, after throwing Queenan off the top of the building, the state troopers are firing at the van. One back window is shot out, then in the next shot of the van the other window is shot out and then the same one is shot again so the one window is shot out twice in the same scene.
Revealing mistake: ***SPOILER*** When Costello is killed, a blood-pack is noticeable under his shirt.
Continuity mistake: When Billy Costigan is at the funeral near the beginning of the movie and reads the card signed "From Frank Costello," it is initially seen as a heavy bold script, but in the closeup, it is a thin script written in different handwriting.
Continuity mistake: When young Sullivan is at Mass, a priest is swinging the smoking incense burning. In the next shot the smoke is gone, and he is away, arriving with the burner and repeating the previous movement.
Continuity mistake: When Costigan is with Madolyn in her office, the tissues in the tissue box change consistently between shots.
Continuity mistake: At Billy's mother's funeral, the signature of Frank Costello on the flowers changes between shots.
Continuity mistake: When Billy and Frank are sitting in a bar, Billy is just sitting at the table. In the next shot he's suddenly in the middle of blowing smoke rings into the air.
Continuity mistake: While Costigan is having coffee with Madolyn, a coffee cup suddenly appears in his hands close to his mouth, and the toothpick that was in his mouth a second ago vanishes.
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.
Answer: It is called "Shipping Up to Boston" by the band The Dropkick Murphys, from their "Warrior's Code" album.
Vin15Nets