Revealing mistake: When the guys are by the half-track keeping Shultz busy, if you look just above and to the left of Shultz's head, you see some tall fencing at the top of the hill in the distance. From the set up, if appears to be a baseball field outside of the studio property.
Revealing mistake: When the men are in the yard during their exercise period playing football, there is a wide shot of the yard. The half-track is to the left of the screen with Shultz next to it. If you look above the barracks, the Desilu water tower and a large metal building, possibly a studio building, can be seen.
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.