Continuity mistake: During the chase scene on the bridge involving the tank, two cars (silver Toyota Corolla hatchback, licence NE34 12 and a black VW Bora, licence NU67 67) appear during many shots, often travelling in different directions on the bridge and either ahead or behind the chase.
Factual error: Brian mentions that the engines in Shaw's flipcars sound like the engines you hear at Le Mans, turbo diesels. These cars have over 500 horsepower and are capable of reaching speeds upwards of 250 miles an hour. They also weigh less than one ton. Shaw's cars seem to meet all these demands: massive power and torque, no body fat and very fast. But here is also a problem: Dom is easily able to keep up in a factory-tuned BMW, which would be nearly twice as heavy, and Hobbs is able to keep up in his "four-wheeled tank", which would be thrice the weight, with even less power. There is no way that an extremely good driver like Shaw wouldn't be able to lose them with such an advantage in terms of power to weight ratios.
Character mistake: Tej mentions that the BMWs they used were factory-line, ie. unmodified. Hobbs then says that they were twin-turbo V8s "spitting out 560 ponies". The BMW M5s they have are E60 models (2005-2010) powered by a naturally aspirated 5.0 liter V10, producing 507 horsepower.
Continuity mistake: During the scene where the cable is shot into the sides of the cliffs to stop the convoy, there are no civilians in the area. As soon as the convoy hits the cable and stops, you can see two normal cars just feet away from it. Not only were the cars never there before, but they would have also gotten stopped by the cable.
Continuity mistake: When Roman is fighting the guy on the bonnet of Shaw's Land Rover, Tej signals him to get back on his Mercedes jeep. When Roman does this, the jeeps are pressed up against one another. Then Tej rams Shaw's Land Rover into the jetwash of the plane. Right before he does this, suddenly a massive gap has appeared between the cars.
Factual error: In the scene where Shaw is talking to a goon while fixing his car he states the simplest things cause the most problems while holding a spark plug. We know this can't be right as Brian concludes the car is a turbo diesel like a Le Mans car, which would actually use a glow plug and not a spark plug.
Revealing mistake: The truck Roman and Tej are suspended in during the runway scene has no prop shaft attached (without it, the truck won't be able to drive at all). When you look at the bottom of the truck while it's in the air, you can see where the shaft was supposed to be attached to the rear differential.
Factual error: When the Mercedes jeep hits the wall at the end of the plane, Shaw goes straight through the windshield and falls to his death in a cloud of shards. Windshields on modern cars, like that jeep, are made out of laminated glass, layers of glass and plastic, precisely designed to prevent shattering into those deadly daggers during an accident and kill the unlucky guy in front of it.
Plot hole: Shaw is let go from custody with the chip because he has Mia hostage. After he's released, he tries to call his guy to finish her off anyway, but can't, because Tej has blocked all cellular transmissions. No reason why Tej couldn't do that while they had Shaw and his men captured and handcuffed.