In the bar scene Will has a glass of booze in front of him. It keeps changing from full to 1/2 full as the camera angle changes.
When Will and Ben are crawling underneath the barbed wire fence
to get into the air force base, there is a ripping sound from the back of Ben's pants. But in the next scene, when Ben is shown from the rear, there is no tear in his pants.
When Will visits his sergeant at night, the sergeant's dog tag keeps changing location on the chain around his neck. This change takes place 5 or 6 times, first when the sergeant is sitting on his bed, then continuing when he stands and accompanies Will to the latrine.
[CLOCKS NOT WORKING] When Pvt. Will Stockdale is in the Classification Office getting classified none of the wall clocks are working. The first thing noticeable was the red second hand not moving. The second was the time. When Will returns to the office after spending several minutes seeing the psychiatrist, Maj. Royal Demming, the time did not change.
The movie has Will and Ben being drafted into the Air Force and seeking transfer into the Army infantry. At the time the movie was made, by law draftees were automatically assigned to the Army for two years (e.g., Elvis); the Air Force has never had to use the draft since it became a separate branch of the service in 1947. The original novel and play that the movie is based on did have Will drafted into the Army during WW II and seeking to transfer to what was then the Army Air Corps, but the film was set in 1958, when interservice transfers were no longer being done.
Throughout the movie, the lowest ranking personnel are referred to as Privates and Corporals. But when the Air Force became a separate service in 1947 (about 10 years before the time depicted in the movie), the names of the ranks below Staff Sergeant were changed to Airman Basic, Airman Third Class, Airman Second Class, and Airman First Class. The general term Airman is appropriate for all of these, and should have been used instead of Private and Corporal.
When General Bush and General Pollard meet, General Bush is wearing a hat with general officer embellishments on the brim, known as "scrambled eggs" in military parlance, but General Pollard's hat does not have scrambled eggs on the brim, which is incorrect, since all officers of Major or above for Army, Air Force, or Marines would rightly have scrambled eggs on the brim.
The members of the B-25 crew are dressed in office uniforms consisting of matching shirts and trousers, plus ties. They should have been wearing one-piece nylon flight suits.
Major General Pollard is shown wearing his medals while on routine duty. Unless it were a formal or ceremonial occasion, he should only be wearing his ribbons, in lieu of the medals they represent.
Behind the movie's credits is a set of Army sergeant chevrons. But all the sergeants in the movie are Air Force.
When Will is in the plane trying to help Ben with the radio, he very clearly has a 'wedgie' as it fills the frame. A moment later, you can see his hand fix the pants problem, as he moves to his right and bends over to talk to Ben.
Dick Wessel, who plays the drunken Army private at the Purple Grotto was 45 years old at the time the movie was filmed. He wouldn't have been accepted for enlistment at that age in peace time, and if he had enlisted when he was younger, his lack of advancement would have resulted in his discharge.