Other mistake: Usually, the picture at the podium has the microphone "bug" for Hogan, and it's blatantly obvious, except to the Germans. This time, there is no bug, but an extra picture that the boys can take the eyes out of and listen in.
Revealing mistake: Every time they go to destroy a truck convoy, you can see that it is a miniature set with model trucks blown up, and it is a re-used shot every time. Same goes for the trains that get blown up.
Continuity mistake: Carter and Hogan are in Klink's outer office when Hogan takes a piece of paper off Carter and folds it into a square. Klink arrives and grabs the paper which has now unfolded to a rectangle. (00:09:10)
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