The staff car that Marya and Schultz are in when they come into camp has its steering wheel on the right side. German cars have their steering wheel on the left.
The chalk map drawn on the truck door in the introduction has 'Carinhall' spelled with a 'K' at the beginning.
When the car with Sgt. Schultz disguised as Goering drives up to the guest building at the stalag, a palm tree is visible in the far distance directly over the roof of the car. As might be surmised, palm trees are not native to Germany.
When Hogan, Klink, and Marya are in Klink's office, Marya tells Klink to send orders in Goering's name to have the art collection brought to Stalag 13. Marya says, "Give them better care than your desk, eh, Klink?" Hogan then turns and moves toward the door, BEFORE Marya turns toward the door and says, "Come on, Hogan." Klink had not dismissed him/them, and Hogan had no reason to head toward the door at that time. He should have waited until Marya turned and gave her line before turning toward the door.