This isn't exactly what you were asking for, but there was one especially proficient German anti-aircraft crew during WWII that played an unintentionally highly significant role in the war. Throughout 1943, British scientist R.V. Jones had been covertly tracking German progress on the development of the V1 flying bomb; although they had pieced many of the clues together and knew roughly what the bomb would be capable of, they did not really know exactly where it was in its development cycle and how soon they could expect the things to begin dropping on London.

In the Fall of 1943, R.V. Jones received word from Ultra intelligence that a company of the highly-regarded Air Signals Experimental Regiment - a group that specialized in radar tracking of incoming Allied airplanes and that he had ordered a specific watch on to detect any unusual deployments - had been relocated to the Baltic coast near Peenemünde (already known to be the location where the flying bomb was being developed).

The company soon began regular radio broadcasting of tracking information using a simple (non-Enigma-encrypted and easily deduced) code that Jones had encountered the Germans using years previously. The tracking data showed objects taking off from Peenemünde and flying generally northeast at 400 mph until suddenly stopping over the Baltic. Quite unknowingly, this German radar company was providing the British with real-time reports on the accuracy of the V1 guidance system (which was, to Jones' temporary relief, terrible at this point in time, assuring the British of some breathing room).

Source: R.V. Jones, Most Secret War