Continuity mistake: When Fred drives his car the wrong way during the race, there is an "8" on the back of the car when he squeezes his way through two cars, but in the next shot the "8" has disappeared.
Continuity mistake: When we see a close-up of Fred's car during the race, you can see there are two cars in front of him and there is nothing behind him, yet in the next shot he is being passed by a purple car.
Continuity mistake: When we see Fred and Barney singing "Doo Dah" in the car while on their way to the track, Barney is sitting in a single seat, yet a close-up shot shows him sitting on a longer seat.
Continuity mistake: When Fred goes past Wilma into the living room to watch TV, he has a fish sandwich and is carrying a tray with a drink and a bowl of snacks on it. When he is watching TV, the bowl of snacks is nowhere to be seen.
Continuity mistake: When Fred drops the tyre on his foot, he hops around in pain and you can see that Barney is holding the tail on the turtle. When Fred says, "Now you tell me!" we cut back to Barney, and the turtle has gone.