Continuity mistake: During the police car challenge, Richard Hammond is taking his homemade police car around the track on a timed lap (with extra points for flamboyant driving). As he rounds the Hammerhead corner, the makeshift stinger (that's a spike strip for the colonials) on the front of his car breaks off and is left behind. He then drives through a stack of boxes, getting one caught on the remains of the stinger mounting. As he approaches the second-to-last corner, the box has gone and the stinger is now back on the front of the car. In the final shot as his car limps across the finish line, the stinger is once again missing and the box has returned. Clearly footage from a different lap was substituted in.
Continuity mistake: During Jeremy's timed lap in his police car, Richard and James watch him go from the start/finish line. But, when James comments about Jeremy having unbalanced the wheels, they are standing in a completely different part of the track. They then return to the line as Jeremy finishes.