Continuity mistake: When Brian drives up to the street racers meeting in the alley, there is a pipe of some sort hanging from his engine. When he picks Toretto up, it's no longer there. (00:10:00 - 00:24:00)
Continuity mistake: At the end of the film when Dom flips it the Supra has a full roll cage, but in every other scene it's only a yellow half cage.
Other mistake: When Brian shoots Tran, two bullet wounds appear in his shirt at the same time, which is impossible, because he was only shot by one person with a handgun. They also appear way too late.
Revealing mistake: When Dom crashes his Charger into a semi, the semi is approaching in the shot from behind the Charger. When the camera angle changes to the front view, the semi is stationary. In this shot, the semi has no front left wheel, and as the Charger passes through the hood of the truck, there is no engine in the truck.
Revealing mistake: During the high-speed chase with the tractor trailer, Vince fires one grappling wire through the truck's passenger windscreen to pull the glass out. He fires a second grappling wire through the now-open windscreen and grapples the passenger seat, then attaches the grappling wire to his harness and leaps to the front of the truck. So, his only tether to the truck is the horizontal grappling wire attached inside the truck cab. But, when the truck driver slams on the brakes, Vince is catapulted around the truck's front-end to the side door, his full weight suspended from a visible, vertical line that is attached to something several feet above the truck cab. The taut line from above even crushes the truck's side-view mirror under Vince's weight. This is the stuntman's safety cable, attached to an overhead boom mounted out-of-frame on top of the truck rig.
Continuity mistake: When Dom and Brian are back at Dom's place right before Jesse gets shot, there are blood stains on Dom's shirt. The stains seem to change during the shots between Dom and Brian.
Other mistake: When it shows SWAT getting ready atop a parking garage to raid Johnny Tran's house, there is a shot of a SWAT officer, in an aiming stance with an M4, but his gun has no sights or scope.
Revealing mistake: When Brian spins the Supra to go after Dom at the end, there are tyre marks from previous takes visible. (01:31:00)
Continuity mistake: Just as we see Dom's Civic get shot, there is a shot of the track driving along. In this shot, Vince is not on the truck. (01:22:10)
Continuity mistake: At the end, as the crew go for the last hijacking, we see all the cars driving over a bridge. However, the railings that are on the side of the bridge are not visible when we see the inside of Leon's car. (01:17:40)
Continuity mistake: When Tran and Dom are arguing at Race Wars, the distance between them changes instantly. (01:11:10)
Continuity mistake: When Dom walks out of the parking garage, he puts his hand to his mouth. Camera cuts and his hand is down by his side. (00:23:30)
Revealing mistake: Just as the lorry and Civics approach the roadworks there are skid marks on the road from previous takes. (00:02:30)
Revealing mistake: Just as the hijackers gain control of the first lorry there is one shot where you can see down the length of the passenger side of the lorry and the rear doors are open and pinned back. (00:02:15)
Continuity mistake: In the first hijacking, the window is pulled out and the rubber seal hangs from the lorry. Camera cuts to the next harpoon and the seal has gone. (00:01:30)
Continuity mistake: When Brian is calling for the air ambulance, he switches which ear his cell phone is on between shots. (01:24:05)
Other mistake: When Brian is evading the cops after picking up Dom, he comes out of a side street and is honked at by a Volvo station wagon, which then ends up crashing into the cop car following. Thing is, the light was red for the Volvo the entire time, so they shouldn't have been rolling through the intersection, much less honking at Brian like he was in the wrong.
Continuity mistake: When the first street race takes place with the four cars, it is evident that the race takes place along a straight stretch of road. However, when the race finishes, everyone who was at the start line just a minute ago has magically appeared at the finish line, miles down the road.
Audio problem: When Brian asks Harry what he said to Dom, As Brian says "Dom" his mouth doesn't move. You can see his mouth for the "Do". (00:09:30)
Answer: There are two ideas of why the police did not come around. Firstly they might have found out after the car chase that Brian was an undercover cop so it would be more effective to allow him to try and discover information instead of going around and arresting Dom. The other idea is that the police might not have enough to arrest him. Dom was not the one driving when they found him and other than racing, it might be tough to arrest him.
Lummie ★
Cops are usually completely unaware of an undercover cop's identity. The more, realistic reason is that the cop didn't ID Dom and since Brian's car was later destroyed, there's nothing for them to investigate. Afterwards, they might ID Dom, but there's an investigation on him, so they'd leave him alone.