Factual errors: When all the adult staffers of Bunker Hill Academy are loaded onto the bus, we see a Captain and a few other uniformed soldiers. Bache's statement that the Cadet Major is only outranked by the commanding general, then, is untrue. Active military personnel outrank ANY cadet in a K-12 military academy.
Errors made by characters (possibly deliberate errors by the filmmakers): When taking inventory of the armory, the man counting the guns states they are ".45 millimeter caliber 1911's". Colt 1911's are .45acp, not .45 millimeter.