Revealing mistake: As Machine Gun Joe runs slowly runs over a fisherman in a small brook, he stops and "peels out" on his head. You can see a film crewman in the driver's seat doing the actual carnage.
Continuity mistake: As Frankenstein tells his navigator to go check the engine while they're driving, she is only visible from one camera angle, even though she ought to be visible from Frankenstein's point of view as well.
Continuity mistake: In the early part of the race, Machine Gun Joe's car is spun out by Matilda the Hun. As he spins, pieces of his car fly off, and when the car stops you can see two of the six sets of Mustang tail lights has fallen off, but throughout the rest of the movie, the car has the six.
Continuity mistake: At the end, Thomasina shoots the navigator, but she seems OK just a few seconds later...
Chosen answer: Like the Olympic gold medal winners, the winner gets t.v. exposure, acting roles, product endorsements, VIP treatment into exclusive parties and bragging rights. By blaming the Resistance, that paints them as the villains and keeps the race going.