When Sixkiller is running and shooting with the MG42, the weapon jams, but the sound of bullets being fired continues. The amount of ammunition Sixkiller has for the MG42 also varies from shot to shot.
In the parachute jump, the riser lines were loose and too spread out in the close-up shots compared to the distance shots that showed the lines tight and closer together since the far-away shots were actual paratroopers coming down.
Dregors, the sniper armed with a scoped rifle, and Major Reisman confer as to the range of the sniper's shot and agree that it is around 70 yards. Not only is a 70-yard kill well within the range of any basic infantryman with a standard rifle using iron sights, 70 yards is within the range of a competent U.S. army pistol marksman. There is no need for Dregors and his sniper skill.
In 1944, Sepp Dietrich was first SS-Oberst-Gruppenführer, later Generaloberst. When he speaks with other generals in the HQ, his insignia is visible. If he is a "Generaloberst", the insignia must have three silver stars - one near to the neck, and two near to the shoulder. In the movie, he has only two silver stars on her insignia, and this means only a "General"
The Uniform Code of Military Justice did not take effect until 1951 yet it is mentioned several times in the movie.
Both in the courtroom and in General Worden's office you see a modern American flag with 50 stars; this version of the flag was not introduced until 1960 after the admission of Alaska and Hawaii as U.S. states.
As their plane lands on the German occupied airfield, you can clearly see a bright yellow ambulance and other modern vehicles parked in a car park next to the airfield.