Continuity: The chalkboards in the first classroom scene raise and lower by themselves a couple of times.
Continuity: The location of the writing that Will puts on the chalkboards in the hallway.
Continuity: The flag in Sean's office near the curtain.
Continuity: When Will and Sean are discussing Will's record and how they were both physically abused as kids, Sean's cardigan sweater goes from hanging near his shoulders to being pulled up with his shirt collar tucked underneath and back again.
Audio/visual unsynchronized: When Profr. Lambeau is looking at Sean through the glass in the door in his classroom, his mouth doesn't match what he is saying.
Continuity: Raindrops appear and disappear several times from the car windows of the four friends right before they get into a fight.
Continuity: When Gerald and Sean are talking in the bar, Gerald's scarf disappears and reappears several times throughout the scene.
Continuity: Chuckie's coffee cup switches hands while he is talking with Will at the construction site.
Miscellaneous: Near the end of the movie, Chuckie goes to get Will but he's not there. As Chuckie is walking back to the car, he and the other two guys are wearing T-shirts and tank tops, as if it is warm outside. Yet you can clearly see Chuckie's breath as he's talking.
Continuity: The first lecture is on analysis and has nothing to do with combinatorics, the kind of mathematics that the rest of the film deals with.
Factual errors: The combinatorial problems and solutions shown on blackboards are elementary ones, not the sort that would occupy a Fields medalist for years.
Continuity: When Gerald and Sean are arguing in Sean's office, the picture of the boat is missing. When Will enters and catches them mid-argument, the picture is back in the window.
Continuity: The rear right window during the argument about the double burger.
Continuity: After Will is released from jail and is riding the subway, the scars from his fight disappear, only to reappear in the next scene.
Factual errors: The closing credits thank "the State of Massachusetts". Massachusetts is actually referred to as "the Commonwealth of Massachusetts".
Continuity: Cigarette in Chuckie's hand when Skylar is telling the story about the Irish couple.
Continuity: When Will burns his proof of a problem and Gerald puts it out, the amount of burn damage changes from almost completely destroyed (when Gerald first extinguishes the flames) to minimally burnt (near the end of the scene), and various other degrees in between.
Continuity: When Maguire and Lambeau are talking about getting a drink at the next reunion, Lambeau's hand switches from his face to his forehead and back again between shots.
Continuity: The position of Will's right arm before he receives Sean's phone-number.
Continuity: In Sean's study, Will has his foot on the desk, but in the overhead shots he has his calf on the desk.
Continuity: When Will and Chuckie are talking over a beer at the downtown construction site, clouds suddenly fill the what was a crystal clear sky halfway through the conversation.
Factual errors: When Professor Lambeau is interrupted at the alumni cocktail reception, the alumni wearing the red jackets are all too young to be wearing the he "Artillery" Red jacket, which is the MIT 50-year alumnus jacket.
Boom mic visible: When Will is given his new car, the microphone can be seen reflected in the window at the right bottom side of the screen
Continuity: At the end after Will leaves and Chuckie goes to pick him up and realizes he's not there, while he's walking back to the car he tells the other guys that Will's not there. However, it can be seen from his lip movements that this is not what he actually says.
Errors in geography: When Will takes the red line train home from MIT in Cambridge to South Boston, he passes through Dorchester, which is past South Boston on the red line.
Revealing mistakes: In the scene where Skylar and Will are sitting at a table with the chess players behind them, the white noise in the background of the shot lessens for Will's line "and I can't play the piano" and the intensifies again afterwards. If you listen closely, you can tell that the one line is a voice over.
Errors made by characters (possibly deliberate errors by the filmmakers): When Sean and Gerald are talking in the bar Sean mentions Einstein and how the world would have looked if the Swiss got drunk in Vienna bars every night. Vienna is not in Switzerland, but in Austria, nor did Einstein reside in Vienna at any point of his life.
Continuity: When Chuckie is having the conversation with Will about how he wishes one day Will wouldn't be home when he comes to pick him up, he finishes the scene with a sip of beer from a can. The can is in his right hand as he takes the sip, but in the next shot as he lowers the can from his lips, it has miraculously jumped to his left hand.
Revealing mistakes: When Sean tells Will about how his wife used to fart all the time, even in her sleep, everybody is laughing. Even the cameraman. The camera starts bobbing up and down at two very funny moments during that dialogue.
Errors made by characters (possibly deliberate errors by the filmmakers): After Will solves the second problem that Professor Lambeau puts on the chalkboard in the hallway, Lambeau and Tom look at it and Tom mutters "looks right". The problem is one that Lambeau and his associates know the answer too, so why does Tom say "looks right"? Either it is right or it isn't.
Revealing mistakes: The person at the bar being served looks at the camera.