Near the end while Schultz is sitting in the chair holding a machine gun on the prisoners the shot over his shoulders shows him holding an MP-40 but when the shot switches to show Schultz he is holding a Thompson and when the shot switches again to over his shoulder he is holding an MP-40 again.
Position of Col. Klink's hands when offering Sgt. Schultz a cigar. Update: When Klink first opens the cigar box (view showing Klink from the front), Klink's left hand holds the lid, and his right hand supports the box. When the view shifts to behind Klink, Klink's hands are reversed. When the view shifts back to show Klink from the front, both hands are supporting the box. The view then shifts back to behind Klink, and his right hand is again holding the lid, and his left hand is supporting the box.
When Schultz and Klink are telling where they were when Poland was taken, Klink walks around the desk to sit in his chair. He is holding his drink in his right hand. When camera changes to close-up, the drink is in his left hand.
During the diversion, Klink calls for water. Carter and Hogan each have a bucket of water. They nod to each other, and start to throw the water (at Klink). The view shifts from Carter and Hogan to show Klink, and only one bucket of water is thrown on him.
Schultz is awarded the Iron Cross 4th grade. The WW2 Iron Cross was only awarded in two grades, 1st and 2nd.
In some scenes in Klink's office, there are heavy shadows from Klink on the wall behind him. This means that some of the strong production lights were to the upper right of the camera.
During the award ceremony, General Kammler says that he and Schultz have been friends for 20 years. When he first arrived at Stalag 13 he said that he and Schultz were at the Battle of Liege together. The Battle of Liege was in August 1914, so their friendship is closer to 30 years, presuming that this takes place sometime in 1943.
Carter is not married, yet when he is working as a waiter at the party, he is indeed wearing a wedding ring.
In the introduction, Hogan mentions that they are paying the motor pool sergeant 10 cents per mile. Being in Germany, which uses Deutsche Marks for money (1 D-Mark is broken down into 100 pfennigs) and measures distance in Kilometers (the car's odometer almost certainly measures in Kilometers), Hogan should have said they are paying the motor pool sergeant 10 pfennigs per Kilometer.