Plot hole: In this episode Arthur scams Deacon and several other parents for phony piano lessons because he doesn't actually know how to play the piano. However, earlier in the series (Art House episode, S1 - E24) we learn that Arthur can play the piano when he temporarily moves out and after his house warming party Doug says to Carrie, "Who knew Arthur could play the piano like that?"
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Revealing mistake: When Doug and Deacon are driving round trying to find Gabe's Pizzeria, they get into the car and pull out into the road. However if you look at the traffic, they would have hit at least 2 cars in doing so. But they don't, showing it's a projection.
Continuity mistake: Carrie tells the preacher that she and Doug met at a bar. When she hears the lie about her falling on Doug as a kid, she believes it and acts as if that was their only meeting before the bar. But in the episode "Road Rayge", she mentioned a junior high school dance where Doug asked her to dance.