Character mistake: When ordering Schultz to finish cleaning his car, Klink salutes Schultz, his returning the salute with the garden hose in his hand leads to Klink being soaked. A salute is, except in rare circumstances, always initiated by the lower-ranking individual and returned by his superior, not the other way round. This rule is broken especially by Klink in several other places as well.
Other mistake: Carter is washing things in front of the barracks. There is snow on the ground and on the windowsills and they are wearing winter jackets but the cold weather doesn't bother him putting his hands in the water over and over. He even gets splashed in the face but it doesn't faze him.