Other mistake: When the boys cause a mini tremor by blowing up the girls' base, the time at which it occurs is strange because when they do it, both Stan's parents are at home (even though they both have jobs), Ms. Choksondik and Mr. Mackey are at Choksondik's house getting it on (indicating that school is over) and the other teachers are still at the school.
Continuity mistake: In the episode "Cat Orgy" when Sheily's boyfriend, Sklar, are playing the song for Sheily while Cartman is hanging on the coat rack you can see of what looks like a picture of Cartman's grandparents hanging on the wall. But when Sheily walks over and flings Cartman up into the ceiling for arguing with her, look at the wall, the picture is completely gone.
Continuity mistake: In the classroom scene where Kyle tries to be excused from class to find Ike, Cartman sets Pip on fire as he was sitting just behind him to the the left. However in the previous shots Pip had not been sitting there, some other kid was and wouldn't have had enough time between shots to move.