Other mistake: When Earl meets with Kimmi in her room, she's supposed to watch "You've Got Mail" - her TV, however, is switched off.
Character mistake: While filming the cheerleader performance, Jasper refers to his inability of using computers ("We're gonna put this on YouTube as soon as one of us figures out how to use a computer!"). Earlier in the series, however, Jasper ordered himself a Russian wife online, so this statement is definitely off-character.
Answer: The premise of the show is he atones for mistakes he did in the past. Winning a car for Joy probably atones for something he did wrong regarding her in the past.
Rob245