When General Hans Stofle is first introduced, he is described as the commander of the famous Afrika Korp. Later, when he is about to be arrested by the Gestapo, he claims to be the commander of the 9th Panzer Division. Correction - he claims to be the commander of the 9th ARMORED Division, Afrika Korp.
At the end, when Hogan is in front of Klink, Klink pulls a cigar out of the box. Hogan picks up the cigar and waves it around. When the view cuts to a close-up of Hogan, the cigar has flipped in his hand.
Nothing was stated as to what happened to the general's girlfriend. The last that was seen of her was that she was passed out on the sofa.
Major Zolle describes the flashlight as being so bright it can find a prisoner 1000 yards away. Since Germany uses the Metric System, he should have said 1000 meters away.
As Major Zolle is demonstrating the flashlight to Klink, he shines it right in Klink's face from maybe one foot away. If the flashlight were as powerful as the Major claimed, Klink would have been blinded by the light, yet he doesn't react to it.
Major Zolle says the listening device can hear a mouse's heartbeat at 100 paces. If it were that sensitive, when he is using it, he would be hearing his own (and Schultz's) footsteps, the sound of their voices as he talks with Schultz, and the clanking from all the equipment Schultz is carrying.
The two Gestapo sergeants are investigating a vent in one of the buildings. There is no way they would ever have allowed any prisoner(s) to hold their equipment while they checked the vent out.