After the killer steps out of the shower, he alternates between being wet and dry.
The son of the killer says, while doing homework/extra credit, that he's practicing multiplication while the rest of the class is still on long division. The usual procedure is to know multiplication before knowing long division, therefore he would not be head of the class, rather behind them.
The school nurse drove David home because he wasn't feeling well. No school nurse, or any other school employee, would be allowed to drive a student home.
The chess board is not set up correctly.