The helmet of the Lieutenant (played by Ken Lynch) has a vertical white stripe on the back. In 1943, the US Army did not use the white stripes during the North Africa Campaign (vertical for officers, horizontal for NCO's). These were not added to the combat helmets until just before D-Day in 1944.
No paratroop unit in WWII was carrying as many Thompsons as shown in this movie. A squad would typically have carried a mix of M1 Garands, possibly carbines, M1919 MGs, and Thompsons. Maybe 1 Thompson per squad.
Also, radios and generators were dropped in supply bundles, not with individual troopers.
Also, radios and generators were dropped in supply bundles, not with individual troopers.