Character mistake: When Hogan addresses him, Major Kiegel sends the girls away from his table by saying "Raus!" The word "raus" used as an imperative literally means "out" in the sense of "leave the room" - he would be ordering the girls to leave the tavern, or at least the tap room in this case. It's not correct German to use it to send somebody away from a table.
Deliberate mistake: When Schultz drives off with the motorcycle leaving the sidecar behind, you can see that the sidecar has been propped up. It has to be, or it would fall over. Sidecars, bringing only one wheel to the party themselves, can't stand up on their own.
Continuity mistake: As the ambulance leaves the hotel, there is snow on top of the fenders and spare tire. Back at the truck, there is snow on the fenders, but not the spare. This would be impossible as at the speed driven, the snow would have blown off any horizontal surface.