When James and Richard land in Lille, they're supposed to land at runway 18, but they land at runway 17. In addition, the runway is the same one they took off from in Italy, which can be seen from the markings on the ground.
In the Bugatti Veyron race, Jeremy jokes that engaging the Veyron's top-speed mode is like moving from DEFCON 3 to DEFCON 4. In fact, higher DEFCON (Defense Readiness Condition) numbers imply lesser danger; he should have said DEFCON 2 instead of DEFCON 4.
In the Bugatti Veyron versus the Cessna 182 race, when the plane is taking off, the shot looking through the windscreen is flipped (the "17" on the runway is backwards).
In the Bugatti Veyron versus the Cessna 182 race, when Jeremy arrives back in Britain, the first shot of him driving on the motorway is flipped (the white van that passes him is driving on the wrong side of the road). Later, the same shot is repeated, but it's the right way round this time.
In the Bugatti Veyron versus the Cessna 182 race, when Jeremy comes out of the lift on floor 21 in the NatWest tower, he goes into another lift and the floor indicator shows he's reached floor 26. When he's next seen, he asks the women how to get to floor 42 from the same lift and the floor indicator shows he's now on floor 23.
When Jeremy first stops for petrol, he says the Veyron's engine has 10 radiators, but he only points out nine.