After they return to the garage from delivering the package to Verone (cigar), they are shown pulling up by the front door. Notice how the road is shaded from the sunlight in front of the garage. Then as they are walking back to the garage itself, the sunlight comes from another direction, illuminating the road and garage front. Also the yellow f-150 Lightning parked there has the front wheels straight, whereas seconds before they were turned.
When the cops chase Brian after the first race, Agent Markham gets out of a squad car and shoots an electrical mechanism to disable Brian's car. Brian looses control and knocks over a parking meter. When he hits it barely any damage is done. In the next shot when the camera pans over his car, you can see that the hood is buckled, and the whole front end is basically destroyed (i.e the missing headlight, air dam and grille area). This damage to the car was done during an outtake, when Paul Walker crashed by accident.
When Rome and Brian are going to the impound lot, Brian breaks the gate to the entrance. You can see the front of his car receiving damage, but when they stop and get out of their cars, Brian's car has no damage at all.
Whilst driving the Mitsubishi Evo there is a shot of Brian changing gear and dipping the clutch pedal. The shot used is of the pedals (with GTR logo) from the Nissan Skyline shown earlier and not of the Evo.
After the scene at the lockup, where Brian says, "Yo, let's break", and the cars begin to leave, we see the Spyder leave, and the driver is wearing orange. Yet when the cars are pulled over by the cops, and Tej and Suki climb out, Suki (driving the Spyder) is wearing black and Tej (Evo) is wearing orange.
in the trailer park scene, there is a Silver Dodge Durango used. however 2 different model years/eras are used in different shots. when the truck is parked in the first few shots, there is no "Durango" badging on the front door, making that Durango a 2001-2003 model. however when the character puts a rock on the pedal the dash is from a 1998-2000 model, same with when it races down the road.
When Brian and Rome are sitting at the table with Carter after Brian and Rome win the tryout race Carter opens the package Brian and Rome retrieved from the impound lot. It is a cigar and he cuts and lights it. The next shot shows the cigar with a large amount of ash already built up, more than could have been smoked that fast.
In the first drag race between the Skyline, Supra, RX7, & S2000. Half way through the race they all round a corner and before the camera changes angles. The Supra was on the inside, followed by the Skyline on the outside. Behind them the RX7 was on the inside and the S2000 on the outside. As the camera changes angles the two cars in the rear rearrange spots. The S2000 on the inside and the RX7 on the outside.
When the Supra jumps the bridge on the first race it is clear that in the shot just after it lands the front rims are that of a stock supra which are smaller and different in design to both the rear rims and the front rims in the other shots.
in the freeway scene where the police chase Brian and the other character, the shots of the cops inside their cruisers, the vehicles used are Ford Crown Victorias. in the outside shots, the cars are clearly Chevy Caprices.
During the struggle with Enrique and Brian right after the money is dropped off, bullets are shot through the windshield. When Rome and Brian go out to see Verone's yacht taking off, behind both of them is the Camaro with the windshield in perfect shape.
When Brian and Roman are racing to find the Ferrari at the beginning of the movie. A red Mustang tries to follow them through the semi trailers. As the Mustang clears the rear of the trailers, the shot switches back to show the trailer wheels. As it does, it clearly shows that the vehicle filming the shot is towing a trailer. The Mustang doesn't even have a trailer hitch.
In the final scene with the blue car and boat. The car is shown to be traveling at 120 miles per hour, but losing ground to the boat. Boats like this are only capable of about 42 miles an hours. If the scene were accurate, the car would be shooting past the boat by about 80 miles an hour and would have been well ahead when it made the jump.
In the 'turbo-charged prelude', we see the now-rogue Brian O'Connor on national news, including reported sightings of him. It seems odd that a crime lord of Verone's standing wouldn't have watched the news for the past few months, and simply recognize O'Connor when he sees him.
After Brian and Roman get the Camaro, Brian puts it on a lift at Tej's garage and, inspecting the undercarriage, says, "This thing is clean." However the camera clearly shows one of the two exhaust collectors is completely disconnected, something any car expert would notice immediately.
When Brian is trying to pull out the electric claw that is lodged in the passenger door, he has his foot on the gas pedal. Brian's foot is barely pushing the pedal and that is also why his car is slowing down.