Deliberate mistake: Lily was an infant for all of season 5, but beginning with this season, she is around 5 years old. The show didn't jump forward in time, because JT states in a season 5 episode that he is 19, and in the episode this season where he and Rich go to Mexico, he states that he is almost 20, as well as Al and Mark are both still in high school.
Deliberate mistake: When Jill turns off the light to Randy's room, she uses the same switch that Al used to activate the reverse laundry chute.
Red Rackham's Treasure - S1-E5
Deliberate mistake: Haddock draws an X on the shark image of Calculus' box with a pencil. This was done as a visual gag, though the X mark is far too thick for the pencil that Haddock was using. (00:07:00)