Continuity mistake: After the beach scene, Costello is preaching young Sullivan on loaded guns. His cigarette disappears from his lips between shots.
Continuity mistake: When Costello is getting his money in the diner, young Sullivan is first sitting next to some packages on the right of the screen , but a shot later, when he stands up holding a brown paper bag, he is seen sitting next to to an empty seat.
Continuity mistake: When Billy and Costello are talking in the bar, after Costello fires the paper cloth, smoke is visible in the shots involving Billy, but not in the ones involving Costello.
Continuity mistake: When Sullivan and his pal are watching the golden dome building from a bench, from a back shot his friend has his head faced straight, but from the front shot it's sideways.
Continuity mistake: The dead woman on the beach lies with her feet together, but a shot later they are spread apart.
Continuity mistake: During the opening scene at the diner, Costello places a comic book in the grocery bag, and it is well below the top of the bag. In the next shot of the bag, the comic book is much higher in the bag, and in fact is almost rubbing the boy's cheek.
Continuity mistake: When Costello is hitting Costigan's broken wrist, as Costello is leaving the room, the shot shows Costigan crumpling to the floor beside the pool table. He is on the floor as Costello is leaving. But, the next shot shows him back on the pool table crumpling to the floor again from a bird's eye view.
Continuity mistake: When Costello and Sullivan are in the porno theater, Costello's line is "it won't be me who suffers for it."When the tape is played back to Madolyn later, it says "it won't be me who pays for it."
Continuity mistake: When Costello tells the girl he has a hard-on, the position of her fingers on the blue book keep changing.
Continuity mistake: While having dinner, from a side shot we see Sullivan's mouth chuckle. Frame later, from the front, he is serious and smiles half a second afterwards.
Continuity mistake: Just after Billy Costigan is shot, the elevator doors try to close. In the shots where the black guy comes out of the other elevator, the doors aren't moving anymore.
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 Sullivan is analysing the Providence corpses, the close-up shows both of his hands together, but on the wide shot one is near the corpse, and the other one close to his hip.
Continuity mistake: After Costello smashes Costigan's wrist he hands all of the dollars he has in his right hand. A frame later money reappears in the hand.
Continuity mistake: When Billy is sitting inside Queenan's house, the glass of water is in his hand in one shot, disappears in the next and then returns.
Continuity mistake: The position of Madolyn's spoon while eating the chocolate cake is not continuous in the front and back shots.
Continuity mistake: When Costigan is with Madolyn in her office. Madolyn doesn't have jacket on but when she runs out after him to give him a prescription she has a jacket.
Continuity mistake: When Sullivan is questioning a bad guy, he sits down with a cell phone right in front of him. But later on, he reaches out to our left to grab it.
Continuity mistake: After Costigan comes out of jail he visits an old lady. From a front shot she is slightly leaning, her left hand unseen. From a back shot the left hand is standing out over his shoulder with a burning cigarette. It should have been visible from the opposite shot at first.
Continuity mistake: When Sullivan crosses the street there's a lot of people going to the right. From the CCTV recording there's just one person.
Answer: It is called "Shipping Up to Boston" by the band The Dropkick Murphys, from their "Warrior's Code" album.
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