Continuity mistake: In the closing credits, Sean's father was listed as "Major Boswell." However, it was established early in the movie that he is in the US Navy and Major is not a rank in the Navy. Its Naval equivalent is the rank of Lieutenant Commander. Even so, in the scene when he was in uniform he had Navy Lieutenant rank on (which is the Naval equivalent to an O-3 Captain in the other branches of the US military).
Continuity mistake: When Sean Boswell is driving the red Lancer for the first time at the docks, right after the guy in the orange sweater says, "Will someone please teach this guy to drift", Sean crashes the back of his car against a pile of wood, and you can see the spoiler falling on the ground. In the next shot, you see Sean's face, and in the background the spoiler is back on the car.
Continuity mistake: In the school canteen scene when Sean is talking to Twinkie for the first time, the food on Sean's chopsticks and the position of them alternates from being in his mouth to back out or on the table between shots, even though Sean is visible in each shot. Also if you watch his drink he takes a sip and puts the glass down, but in the next shot a second later he is drinking from it again.
Continuity mistake: In the scene where Sean is making his first pickup for Han, from the large man in the jacuzzi, he is dressed in only a towel. When the large man throws him out of the establishment, he is fully dressed. Are we to believe that the large, angered man who Sean just demanded money from, gave him time to get fully dressed before throwing him out? Or that the large man dressed Sean before throwing him out? Neither of these scenarios make sense.
Continuity mistake: At the end of the movie, right before the race against Vin Diesel, the two cars are placed very close, within a foot or two of each other. A couple of shots later, right before the girlfriend says 'Go.', the cars are a couple of feet further apart, even though they haven't yet started the race.
Other mistake: Throughout the movie we see the mustang rolling chassis in the garage. This is a rolling chassis of a 1967 Shelby mustang gt 500/350. The main ways to realize this are that the car has the cut outs in the front for the 2 fog lights that the Shelby had and that the back end has a spoiler which is built into the body. However the car they do all the driving with is a base model 1967 mustang fastback. While a new grille would've covered up the fog-light cutout, the regular fastbacks didn't have the built into the body spoiler like the Shelby's did. Removing the built in spoiler and making it as smooth as it was would've taken way too much time and supplies. It also wouldn't have served any benefit. You could argue they were trying to eliminate down-force on the back but the spoiler was only about 2 inches, it wouldn't have helped. The directors did this to avoid wrecking the much more rare Shelby mustang.
Visible crew/equipment: In the first race when Sean and the rich kid in the red viper are racing each other the rich kid pulls up to the black ute that is following them and yells "whoooo" and puts his fist up, you can see the camera mounted on the side of the viper through the reflection of the black ute.
Continuity mistake: When Twinkie is about to show Sean his car, the garage door opens to show a black car. The car holding mechanism begins turning and Twink is shown saying "no" to Sean. When the camera cuts back, there are bicycles where the black car was. Then, there is a red car next. Twink says "no". When the camera cuts back, the red car is now black. The mechanism isn't going that fast.