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.
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.
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.
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: Tej tells Hobbs he's got this, and the scene changes to establishing shots around London. The first shot shows a shot of London, featuring many landmarks and Big Ben in the background. The time in the first shot is 2:10. The shot changes with the camera closer to Big Ben and the time is suddenly 3:00.
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.
Continuity mistake: During the car chase in London Brian and his team get their cars shot up, but in the following chase the cars show no damage.
Character mistake: Brian compares Shaw's cars to "something you'd hear at Le Mans, a turbo diesel." However, a turbo-diesel is simply a turbocharged diesel engine, fairly popular (and common) in Europe like its non-charged counterpart, due to much better gas mileage and lower price of diesel fuel. On the other hand, WEC (World endurance championship, under which Le Mans 24 belongs) allows lot of variability in engine design. TDI engine was only used by Audi teams and for a short time, by Peugeot. Others used petrol turbo or NA engines.
Factual error: The route Dom and Letty use for their race is not consistent with the sights shown in the background - they are jumping all around the west end of London, then pull up near Battersea Power Station which is south of the Thames.
Plot hole: When the crew is chasing after Shaw and his gang. Shaw's goons plant bombs on their cars. The bomb on Brian's car is in a location that technically Brian wouldn't have even known that it was there. If this bomb was somewhere he couldn't see it, then Brian wouldn't have been able to clip the pole to make it fall off.