When Backscheider breaks down Hogan/Dirken's door, the door frame stays completely intact, showing that the door is designed to break away without damaging the frame. This allows it to be re-installed if the scene requires additional take(s). In other words, the door is not even fastened to the frame.
Shortly after breaking into Hogan's room, Colonel Backscheider is facing the camera while his men are searching Hogan's room. Around the time when Backscheider asks, "You wanted a call from the Gestapo?" the stage lights reflect off the lenses of Backscheider's glasses. The fact that the reflection covers the entire surface of the lenses indicates the lenses are flat on the front side. When Backscheider turns to talk to Hogan, the lenses are completely flat on both sides, and the view of the louvered doors through the lenses is not distorted, indicating the lenses are props (meaning the glasses are merely for show).
Shortly after breaking into Hogan's room, Colonel Backscheider is facing the camera while his men are searching Hogan's room. Around the time when Backscheider asks, "You wanted a call from the Gestapo?" the stage lights reflect off the lenses of Backscheider's glasses.
After Hogan and LeBeau go to Paris, Captain Gruber increases security at Stalag 13, including nightly bed checks. There is no way that Hogan, as the ranking prisoner of war, would not be found missing, causing Gruber to raise an alarm.
After Backscheider breaks into Hogan's room, Backscheider refers to a study where French footsoldiers were only able to march .7 miles. Since Germany was/is on the metric system, he should have said the footsoldiers could only march 1.2 kilometers (or 1200 meters).