Continuity mistake: When Hogan and the crew first see the silent airplane overhead, it has a twin tail. When shown up close in later scenes it has a single tail.
Plot hole: Hogan's men steal the motor from the silent plane. When Klink and Burkhalter inspect the plane, Burkhalter doesn't notice the engine missing. Later Klink doesn't notice the fact that it has been put back. This is totally impossible for two reasons: Firstly, if a propeller airplane misses its motor, there is no place to mount the propeller. Secondly, when we get to see the whole plane, it becomes obvious that it has an open engine cowling which leaves the motor exposed to be cooled by the airstream. The propeller issue aside, if there is enough light to see the hand in front of your eyes, it is impossible to miss either the presence or the absence of an engine inside that kind of cowling. Add to this the fact that both Klink and Burkhalter are Luftwaffe (Air Force) officers and therefore by trade have some experience with airplanes, the whole thing becomes even more ridiculous.
Revealing mistake: At the end, when the boys are in formation and Klink is walking through the ranks, he walks around Hogan's right side. As he does so, you can see LA's Desilu water tower.
Revealing mistake: When the High Command men are watching the "noiseless engine" plane, the camera cuts to a shot of the four of them in the car. To the right (camera's left) of the man in the right side, back seat, you can see LA's Desilu water tower.
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. (As another contributor previously posted, the term "nimrod" is slang for a nerdy, doofus type of person, though it's unclear why that was his code name).
raywest ★