Continuity mistake: Doug finishes playing the tennis game on the TV with Arthur and goes into the kitchen to get the Cheese Doodles. While talking to Carrie, he puts the Cheese Doodle package on the table with a can of cola behind it. He then goes to get a glass from the cupboard and in the next shot you see the cola is in front of the Cheese Doodles.
Continuity mistake: When Carrie confronts Arthur about looking in her bag, her bra strap is slightly hidden by her top. Camera cuts to a front view of Carrie then back to behind her. Now her bra strap has moved and is totally visible. Carrie never touched it during this time as we see her hands.
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?"