Corrected entry: How does the man who shoots Costigan at the end of the film know he is there? Costigan says he only called the cop he knew he could trust, and Sullivan is suprised to see him at the end, so how did he know what was going on?
Correction: Officer Barrigan (who graduated the academy with Sullivan) was also a rat in SIU working for Costello. After shooting Costigan upon the elevator opening, he rhetorically states that Sullivan isn't the only one "on the inside" but also that Costello was going to sell them out to the FBI so now they have to stick together. As mentioned by someone else, Barrigan could have been following Sullivan after Costello's death.
Corrected entry: In the opening scenes, of the execution on the beach, it cuts to the woman lying there. Before the cut French has a gun in his left hand, then after he has an axe in his right hand as well.
Correction: French actually has the hand saw in his left hand and the axe in his right hand throughout the scene.
Corrected entry: In one scene, Madolyn enters the apartment carrying a bag of groceries. She asks Matt Damon if he wants "a French doughnut". When he accepts, she hands him what appears to be a cinnamon roll which he almost immediately sets down. In subsequent shots during this sequence, a plate is visible on the countertop one which can be seen what appear to be some pieces of bread or the like, but no cinnamon roll and definitely not a French doughnut.
Correction: The roll is a croissant. A french pastry, which she jokingly calls a French doughnut because he is a cop. It remains the same throughout the scene.
Corrected entry: When Costigan is beating up the Providence goons, he is hitting the one in the cooler with his right hand. In the next shot he is hitting with his left.
Correction: If you look carefully you can see Billy change hands and begin hitting the Guinea with his left hand. The transition is not inconsistent.
Corrected entry: Sullivan shouldn't have had to yell out that he had Costello after shooting him. The other cops would've surely heard the barrage of gunshots and came running as they had already stopped shooting long before.
Correction: The most likely reason for this was as you pointed out the police would have probably heard the sound of gunshots and have their weapons drawn. Sullivan would be simply taking the precaution to warn the police in case they mistook him for one of the suspects.
Corrected entry: When the psychologist is looking at Sullivan's mail in their apartment, the envelope from Costigan has Sullivan's address listed at 20 Pickering St, Boston, MA 02459 Apt. 711. In Boston there is a Pickering Ave, not Street and there are no 7th floor apartments. All the buildings on the street are multi-family houses no more than 3 floors. It also has Costigan's address listed at 13 Conant St. Boston, MA. There is no Conant St. in Boston.
Correction: There is also no 742 Evergreen Terrace in any Springfield in the US. Addresses in movies are rarely if ever proper addresses to avoid people going to those locations and causing problems. This is a standard movie convention and is not considered a valid error.
Corrected entry: When Sullivan makes the phone call to Costigan using Queenan's cell phone, he leaves Queenan's blood on the talk button. It's been hours or even days since Queenan's murder, how was the blood still wet?
Correction: Because the phone was sealed in an air-tight bag.
Corrected entry: In the scene where Nicholson "hits" DiCaprio's cast with a shoe, he never really hits it. Watch closely, and you'll see him hit the pool table instead each time.
Correction: Indeed, Nicholson does not hit DiCaprio's cast. His assistant does. The force of the blow carries the shoe past the cast after it strikes it and onto the pool table.
Corrected entry: When Leonardo meets with Queenan, it's at 344 Wash. However, when one of Costello's guys calls Leonardo, he says the rat is at 314 Wash.
Correction: That was part of the whole setup to expose the informant. It's a key plot point to the movie, and not a mistake.
Corrected entry: In the scene where Billy visits Queenan at his home, Queenan hands a glass to Billy and says, "Here's some ice water." But there's no ice in the glass.
Correction: Ice water doesn't necessarily mean water with ice in it. At my home, ice water means water that we keep in the fridge in a pitcher to keep it cold.
Corrected entry: In the final scene after Matt Damon gets shot and falls to the floor and Mark Wahlberg walks out of the room, the camera shows Matt Damon lying in a pool of blood. A second later the camera cuts to a different angle of the body lying on the floor and it is no longer Matt Damon. It is a different actor with darker hair, darker eyebrows and wearing different clothes.
Correction: It's still Matt Damon, you can tell from his "V" hair line, and he is wearing the same green shirt.
Corrected entry: How does the man who shoots Costigan when he gets out of the lift know he is there? Costigan only told two men where he was going; Sullivan and his friend from the academy. Sullivan told no one, as we see he is suprised when the man shows up. I know the man says he is a mole within the force, but that doesn't make him telepathic. Only three men knew about the meeting: how did he magically find out about it?
Correction: He could have followed Sullivan or Brown there.
Corrected entry: When Costigan leaves the adult theater and follows Sullivan to get an ID, his phone rings in the alley and this lets Sullivan know he is being followed. This seems convenient to the plot, seeing as how Costigan's phone was just on vibrate in the theater.
Correction: Unless the keypad is locked, on most phones it quite easy to accidentally jostle it or depress buttons in such a way as to change the ringer setting. It happens all the time to me, particularly if the phone is in my pocket. Yes, it's a plot device, but an intentional one that serves to underscore the peril's of Costigan's double life.
Corrected entry: When Costigan is exiting the lift with Sullivan he is shot, but how did the man who shot him know he was there? Costigan only told his friend from the police academy, and Sullivan obviously didn't know the killer since he was suprised to see him and knew nothing about any other moles in the police force. This isn't to be confused with Mark Wahlberg's character shooting Sullivan at the end of the film.
Correction: The man who shot him was also a mole in the force. That's why he said "We gotta stick together".
Corrected entry: After Will leaves the girl's office with the "two pills" she sighs very deeply but her mouth says "f***"
Correction: You can't hear her say "f***" because she doesn't actually say it, she just mouths it on purpose. It's a way for her to let out her anger and frustration, but not have to worry about anyone outside her office hearing her.
Corrected entry: The close up shot of Costigan's phone reads "restricted" in the scene where Sullivan calls Costigan using Queenan's bloody cell phone. Costigan then calls back, saying, "you called me on a dead man's phone!" Amazing how he knew the call came from Queenan's cell based on a restricted number.
Correction: It's not likely Costigan would be making or receiving a lot of calls with restricted numbers. Seeing as he knew Queenan was killed, and he was in Queenan's circle, it's logical that he would assume the number was from Queenan's cell, and that it was Sullivan calling.
Corrected entry: In the scene where Costello confronts Costigan about being the rat in the bar and Costello has walked away and come back for his cigarette, an unlit cigarette magically appears in Costigan's mouth between shots.
Correction: I saw this scene twice and it is not too far out. Not sure why this is a mistake? Pulling a Cigarette out of your pocket only takes a second. Billy puts it in his ear. One shot is filmed with it and one without it but it does not seem out of the ordinary.
Corrected entry: During the first meeting of Billy(DiCaprio) and Madolyn (Farmiga) in her office, the computer behind her initially shows a McAfee update notification in the bottom right hand corner. And the camera flicks between the two of them it disappears mid-scene, yet reappears again towards the end.
Correction: Those particular McAfee notifications do not stay on screen for long. They pop up in the corner, then they disappear. If the user gives no attention to the notification, it pops up again. Obviously she had no time to bring attention to it, therefore it proceeded to come up again on her screen.
Corrected entry: In the scene near the start of film where you see Matt Damon playing rugby, he is seen pushing in the scrum. He is playing in the flanker position. This would mean that he would need the number 6 or 7 on his back. However, when he is walking off the pitch he has the number 10 on his back which would mean he would be playing fly-half.
Correction: Although technically this is correct it is not unheard of for a player in the backs to go into a scrum. If, for example, the opposition back line is lightweight some teams have been known to swap a flanker for a lighter back so that the flanker can make an impact going forward. (Wales have done this in the past with Gareth Thomas).