When Kinch gets the mileage off the odometer, he reads it in kilometers. When Hogan is talking about how far the car traveled, he uses 'miles'. Update: In Hogan's position, he would know the formulas for converting kilometers to miles (and vice versa). Since the maps he is using are most likely American (USA) maps (not captured German maps), he would be working in miles, not kilometers.
When the German guard was pushing Cpl. LeBeau into the laboratory with the basket of vegetables, he kept shouting "Raus" to get LeBeau to keep moving. Only trouble is, they were going into the laboratory, and the German word "raus" means "out" in English. He should have been using a word like "vorankommen" ("get a move on") or the ever-popular phrase (used quite often during the series), "mach schnell" ("make it quick").
Ther is no way that LeBeau, while in the trunk of the car, could have heard any conversation taking place in the cab while the car is moving. Between the engine noise, road noise, and the padding/insulation of the rear seat in the cab, he would be hard pressed to hear any of the conversation.
Newkirk, as Dr. Schnitzer, has Schultz go into the prisoners' barracks for the shot. In reality, he would have given him the shot in the infirmary, or in the guards' barracks.
At the end, when the underground laboratory blows up, the ramp/door blows open before the explosion. The door should have blown open at the same time as the explosion, since the pressure wave from the explosion would hit the door only a split second after the explosion - a short enough time span that a human would perceive them as happening simultaneously.
In some of the scenes in Klink's office, a production light is seen reflecting in Klink's monocle.