Continuity mistake: In the final show of season twelve, the Vietnam Challenge, when Jeremy Clarkson borrows James May's bike to try to pass his practical driving test, throughout the test, it can be seen that May's "Darcey Bussell" statue is not on the bike. He then conversed with May and Richard Hammond, still seated astride the bike and "Darcey" is still not present. As Clarkson gets off the bike and lets it drop, still in mid-conversation with no breaks, the statue is suddenly strapped tightly onto the luggage rack, just in time to break on impact.
Continuity mistake: At the end of series 13, after Richard uses a cherry picker to stick a cool wall picture out of Jeremy's reach, Jeremy jams the controls and goes to interview Jay Leno. But throughout the interview, the cool wall is visible in the background and the cherry picker has gone. Afterwards, Richard is back in the same place without having had time to move.
Factual error: During the polar special, when Mattie first gets her kite out, Richard says that they are in the same fjord where Jeremy and James went through the ice. If so, the scenery has changed remarkably in a couple of days. All the blue ice is gone and so are the cliffs, which prevented Jeremy and James driving out. He can't have taken a different route as the fjord is only a mile wide.