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: Nimrod's actual identity was never revealed in the series. It was only known that he was a British intelligence agent. Nimrod was not Colonel Klink. Hogan had only implied it was him as a ruse to get Klink returned as camp commandant, not wanting him replaced by someone more competent who would impede the Heroes war activities. The term "nimrod" is also slang for a nerdy, doofus type of person, though it's unclear why that was his code name.
raywest ★
"Nimrod" is originally a king and hero mentioned in the Tanach and taken into the Bible and the Koran. His name is often used in the sense of "stalker," "hunter," and sometimes figuratively as "womanizer" as in "hunter of women." I've never seen it used to denote a nerdy person, and although I cannot disprove that connotation, I think given his role, the traditional meaning is more likely the intended one.
Doc ★
It's widespread enough that Wikipedia has an entire section on it: https://en.wikipedia.org/wiki/Nimrod#In_popular_culture