The show was shot so that it was always winter, but several episodes feature factual occurrences not in winter. Most blatantly D-Day (in June) and Hitler's birthday (late April).
Klink's promotion to Chief of Staff would have never happened. The position is for Chief of Staff of the Army, and since Klink was in the Luftwaffe, he would have never been considered for the job.
Update: This restriction makes no sense in the context of the episode. If the search for Chief of Staff were actually legitimate (i.e., by Hitler himself), then this would be a valid Factual Mistake. Since this is being engineered by Hogan and the gang, going outside of 'normal' channels is perfectly legitimate.
Update: This restriction makes no sense in the context of the episode. If the search for Chief of Staff were actually legitimate (i.e., by Hitler himself), then this would be a valid Factual Mistake. Since this is being engineered by Hogan and the gang, going outside of 'normal' channels is perfectly legitimate.
(at around 16 mins) Newkirk refers to "General Rommel." Erwin Rommel was promoted from general to field marshal in 1942, before the Normandy invasion referred to in the story. (at around 20 mins) Schultz refers to "General von Rundstedt." Gerd von Rundstedt was promoted from general to field marshal in 1940.
When news of the invasion comes to Klink, and he calls Hitler's headquarters in Berchtesgaden, the implication is that it is the dark of night (the windows in Klink's quarters are dark, and Klink asks what time Hitler goes to bed). The actual beach invasion did not start until 6:30 AM - after sunrise.
After Hogan gets back from London and climbs up the ladder into the barracks (while Schultz is searching for him), the tunnel cover/lower bunk drops down without being activated by anyone.
When Hogan goes to London, the British general pulls down a colored map, briefly revealing the location of "D-Day," the Allied invasion of Europe. However, it shows Germany already divided into East Germany and West Germany, something that did not exist until war's end when the Soviets and the other "western" Allies split Germany into two, separate countries.
From view through bunk towards Schultz when he says "everything has to be", and then sees the lower bunk fall into place, a black cord can be seen moving at the bottom of the top bunk.
In some scenes, there are reflections from the production lights in Klink's monocle and on his bald spot.
Klink and the generals are all in Klink's quarters (temporarily in use by General von Scheider). General von Scheider is looking for his wife, and General Bruner suggests to Klink that a Panzer division should be brought up. When General von Scheider says that the Panzers can only be brought up by order of Hitler, the camera zooms into a close-up of General von Scheider, at which point a shadow of the camera appears on the right side of General von Scheider's chest.