Character mistake: In the opening scenes when Brian goes back to the shop, he demands that he needs some nitrous to boost his low top speed. Well I'm sure that most tuners will agree that more horsepower doesn't equal more top speed, it only contributes IF you have a transmission that can handle it and distribute it. (00:09:53)
Character mistake: When Brian looses the race against Dom, Dom states that Brian didn't know how to drive and was 'granny shifting' instead of 'double clutching like you're supposed to'. Double clutching is NEVER done in drag racing as it requires twice as much time to shift and is ONLY done when down-shifting. It is used to synch the engine RPM with the speed of the wheels but new cars have syncros that do it for the driver. (00:22:00)
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.