Revealing mistake: In the close ups, Professor Bauer's spectacles do not have lenses.
Other mistake: Baker goes to tap the rectangular spot to open the trapdoor, not only does he hit it once rather then twice, but it sticks in the pressed position. A moment later, Hogan hits it, but it stays in the pressed position rather than popping out. The sound of the pressing is played, but the button doesn't move.
Visible crew/equipment: When Major Hochstetter's car arrives at Stalag 13, it drives towards the camera. The shadow of a crewman's hand raised to stop the car is visible on the ground. (00:16:40)
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.