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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Continuity mistake: When Doug and Carrie are in the living room talking about Doug not going out with Kelly again, he has the phone in his hand, gets upset and throws the phone down. Then Carrie is going to call Kelly for Doug, and when she goes to pick up the phone, it's placed perfectly back on the hook when it should be hanging near the floor from the way Doug threw it.
Continuity mistake: In the scene where Danny has just taken the "nucleus" nacho chip, after Carrie walks in, the chip in Danny's hand keeps changing between shots, then disappears altogether almost instantly and his arms are folded when he begins his next line.
Continuity mistake: When Arthur is telling Carrie he has got a job, Carrie is putting out paper plates. She puts all three out and then the camera changes angle. When it does, one of the plates has moved across the table and Carrie is seen placing it in position again.