Continuity mistake: In the construction site scene, you will notice the length of Ben's cigarette fluctuates several times. It actually gets longer/shorter as Ben smokes it.
Continuity mistake: When Will burns the paper, a large part of it is burned (almost the right half). But when the professor grabs the paper from him, a much smaller portion is burned (just the bottom right-hand corner).
Continuity mistake: When they are crossing the bridge to go back into Boston, after leaving the bar in Cambridge, a Red Line subway train is shown and then in the next shot there are several buildings in the background as they cross the bridge. These buildings are in Boston, but this shot has them driving away from the buildings, which means they would be re-entering Cambridge.
Continuity mistake: At the end of the film during Will and Sean's last meeting, there is a shot showing both Will and Sean and we see Will with his hands in his lap. It then cuts to a shot over Sean's shoulder and we see Will, but now his hands are raised and his elbows are on the arms of the chair.
Continuity mistake: When Ben and Matt are sitting at the construction site drinking a beer, Ben takes a sip of his beer with his right hand in a close up. The next shot shows him holding the beer in his left hand, flicking a cigarette with his right.
Continuity mistake: When Will goes to Skylar's dorm room to take her out to "go have some fun" he's wearing a striped t-shirt and blue jacket, while they're out on the date he's wearing a short sleeve button down and no jacket.
Revealing mistake: When Will and Skylar are on their date and eating hamburgers, an extra in a blue jacket is seen walking by in the background multiple times.
Factual error: When Will is telling Gerald that he wants to meet at Sean's office instead, because going to MIT was to far of a commute, doesn't make much sense. Bunker Hill Community College is much more of a commute than going to MIT, especially if you're coming from South Boston on the Redline.
Continuity mistake: In the scene "When Did You Know?", when Will tells Sean that he read his book last night, an aerial shot looking down at them shows Will with his foot up on the table. But two shots later Will has his foot up on the chair instead. The chair in the first shot would also be too far away for Will to reach from his own chair, so that would have been moved in the later shot for him to reach.
Deliberate mistake: Skylar's leaving is edited together with footage of Will sitting in a park watching planes take off - including, presumably, her plane. The sun is directly overhead in his scenes, while hers were filmed near sunset. (Most obvious when you see the very long shadows during the same airport footage which is also used in the deleted scene "Pudge Fisk Card").
Continuity mistake: In the scene where they are all gathered in the bar together Ben is telling the story about his uncle. Throughout the entire scene, Ben has nothing in his hands but as he comes to the end of the story there is a camera shot over his right shoulder showing him holding a cigarette. However, when the next shot moves to in front of him, the cigarette has gone again.
Continuity mistake: At the university in the beginning, the blackboard on the wall changes position in every shot - once it's pushed up, next shot it's at the bottom. Several times.
Factual error: A photograph is displayed of people at a 25th year MIT reunion in which they are wearing cardinal and grey jackets. Alumni do not receive these jackets until their 50th year reunion.
Visible crew/equipment: During the scene where Will has his last therapy session with Shaun, he reaches up to hug Shaun. His shirt in the back rises up, and you can briefly see some sort of small black equipment/cables that look like a battery or mic pack tucked into the back of his pants.
Revealing mistake: When Matt Damon and Minnie Driver are sitting outdoors at Au Bon Pain in Harvard Square, Matt is telling her how he is able to "see" mathematical equations, just like Beethoven was able to "see" the notes on a piano. At one point during the conversation a girl wearing a red backpack (possibly a Harvard student) walks by in the background, stops and looks at the camera, smiles, and then continues on her way.
Factual error: Neither of the two problems that Will completed on the hallway chalkboard were actually proofs. With a "proof," you start with a specific conclusion and show the work necessary to verify mathematically that the conclusion is correct. With both problems on the hallway chalkboard, however, the objectives were simply to calculate and arrive at the answers without knowing in advance what the answers were.
Continuity mistake: The problem on the board that Will solves changes slightly. The scene is a bit apart but you can see the huge change. Once it reaches all the way to the bottom. Other time, it only reaches halfway. One time it had (I think) 1,2,3,and 4 and other time only 1,2,3.
Other mistake: When Gerald and Sean go to have lunch Sean asks his friend to bring them 2 sandwiches, and yet doesn't specify what type of sandwiches, nor does his friend ask Gerald what type he would like. He probably knows what type of sandwich Sean likes but he's meeting Gerald for the first time, so obviously he would have no idea what type of sandwich Gerald would want.
Continuity mistake: The first few minutes of the movie contain classroom/lecture hall scenes - the walls are a very distinct dark brick, and the seats an uncanny orange. This decor is at the University of Toronto, not at M.I.T. where the movie is set.