Goofs

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.

After Will is released from jail and is riding the subway, the scars from his fight disappear, only to reappear in the next scene.

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.

The chalkboards in the first classroom scene raise and lower by themselves a couple of times.

When Gerald and Sean are talking in the bar, Gerald's scarf disappears and reappears several times throughout the scene.

When Professor Lambeau is interrupted at the alumni cocktail reception, the alumni in the red jackets are all too young to wear the "Artillery" red jacket, which is the MIT 50-year alumnus jacket.

The combinatorial problems and solutions shown on blackboards are elementary ones, not the sort that would occupy a Fields medalist for years.

A U.S. Army general sits next to Will during his interview at the NSA. Several aspects of his uniform are wrong: the thick black band that generals wear on their lower sleeve is missing, the non-US decoration under his name badge shouldn't be there, generals don't wear the Infantry branch insignia (crossed rifles) on his lapels, and the braided chin strap above his cap's visor is wrong for any US army cap.

The closing credits thank "the State of Massachusetts". It's actually the Commonwealth of Massachusetts.

The solution Will gave to the second problem, the tree one, is wrong as he missed one of the possible solutions. (3,3,5)

During his trial for assault on a police officer, Will begins to quote Henry Ward Beecher's "Prayers from the Plymouth Pulpit" and dates it to 1887. It was actually published in 1867. Henry Ward Beecher died in 1887, but the prosecutor and judge wouldn't have known that because they didn't know Will was going to use that argument.

Sean orders "a couple of sandwiches." Unless the brasserie serves only one kind of sandwich, the order is much too vague. Sean is a regular, so the owner could have known him well enough to know what he was talking about.

After the verbal confrontation in the bar, the gang leaves and is passing by the restaurant where the blond college boy, Clark, is now sitting with his friends, Will slaps a paper with the Skylar's phone number (555-1294) against the glass, saying "I got her number. How do you like them apples?" In the United States of America, there is no 555 telephone exchange. Historically, a 555 exchange has often been used in movies and TV shows so that real phone numbers won't be called after the movies or shows are seen.

The "straight six" engine in the car that was Will's 21st birthday present is likely a 250 CI 'stovebolt six', and it's longitudinally mounted, as it should be.

At the end of the movie when Chuckie goes to pick up Will, he's wearing short sleeves and shorts. It's probably August or September and the trees still have their leaves. August is still summer in Boston, and warm weather can stretch in to October.

When Sean tells Will his wife used to fart all the time, even in her sleep, everybody laughs. The camera starts bobbing up and down twice during that dialogue. Apparently, the camera operator was laughing, too.

When Skylar and Will are sitting at a table with the chess players behind them, the white noise in the background lessens when Will says "and I can't play the piano" and intensifies again afterwards. The line is a voice-over.

The person at the bar being served looks at the camera.

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.

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.

When Chuckie is at Will's house to pick him up, Morgan gets out of the back seat of the car to change and sit in Will's old seat. While he's climbing into the passenger seat, a crew member with a red hat is visible at the bottom left corner of the screen, watching from the sidelines.

In an early scene, Will says he works as a janitor at MIT because it was part of his probation work placement program. In a later scene, Lambeau questions Will accusingly about why sought out a job at MIT. It may be a misunderstanding between the characters, to demonstrate Lambeau's ignorance toward Will, but it leaves a lot of open-ended questions about whether it was chance or a deliberate path that Will chose.

When Will gets his new car, the microphone is reflected in the window at the bottom right of the screen.

Skylar's binoculars are backward while she watches the dogs at the racetrack.

Skylar's dorm room bulletin board has two British flags, one on either side of the Harvard banner. The one on the left is upside down.

After looking at Sean's painting, Will refers to him as a psychologist. Sean is a psychiatrist.

When Will and Chuckie are in the batting cages Chuckie says, "Casey is bouncing up a bar at Harvard next week. We should go up there." There is no character in the movie named Casey. It seems that Ben Affleck meant to say "Morgan", the character from their friend group played by his brother Casey Affleck, instead of the actor's actual name.