Revealing mistake: The first shot of the train the view is normal. Then after Lebeau starts in reverse you can see the smoke trail going in the wrong direction. The final shot shows the train moving in reverse, but notice the smoke trail is going to the rear of the train instead of the front as it should be, since it's moving in reverse. (00:15:05 - 00:22:25)
Revealing mistake: LeBeau hands Schultz the pan straight from the hot plate, but Schultz puts at least three fingers around it while eating without any apparent issues. Note that LeBeau earlier said the Crepe Suzette were "not quite ready yet" - or in other words, still cooking. (00:01:40)
Revealing mistake: While talking about Von Baler's daughter, Hogan is facing the building talking with Carter and Newkirk. Behind him is an open area of the camp. If you look, you can see that there is no guard in The Tower, no shadow of The Tower of the guard hut (the sun is behind them and Hogan), and the snow is piled up about three feet behind Hogan, suggesting that the background is a wall mural in the studio.
Revealing mistake: The Major goes to shoot out the light that the boys have turned on so Kinch can get the pictures. The first shot is angled too low to hit the bulb, but there is no impact on the front of the door's crosspiece; the smoke and dust comes from behind it. The second shot gets the bulb, but there is no muzzle flash, just sound. Also, there is no impact mark on the brick wall behind the bulb.