Radiation inhibits cell growth, it doesn't accelerate it.
The interior of the aircraft during the parachute drop is illuminated in red. Red lights were only used at night. The drop is during the day.
The captain states the unit landed three miles from its objective, and implies that this is off target. Under the circumstances, landing within that distance of the target would have been considered far better than expected.
When the tank fires on the Doomtrooper it creates no muzzle blast, which would have at least injured the entire unit in front of the tank. The explosion, when the tank round hits, is ridiculously small. A 75mm shell from a Panther (as the tank was supposed to be) would have killed or injured everyone in the street and collapsed some of the building.
The Nazi Super Soldier wears machine guns on his wrists, but the guns do not eject any spent shells.
The female French Resistance leader is carrying a Soviet submachinegun.
There are no muzzle flashes from any of the guns or cannons shot. There are also no spent rounds expelled from any of the machine guns.
The MPs at American headquarters are shown wearing full-color American flag shoulder patches on their fatigues. Those types of patches were not worn on American army uniforms until long after World War II.
A US Army 2-1/2-ton truck (commonly known as a "deuce-and-a-half") is shown driving through the American headquarters base. The truck shown is not the American-made deuce-and-a-half that was used by the US Army in World War II; since the film was shot in Bulgaria it was most likely a Russian-built military truck, but whatever it was, it was not an American one and would not have been used in a World War II-era American army unit.
Bombers are unable to attack the laboratory due to its defense with a radar which had "pin-point accuracy". Yet the C-47 troop carrier flies well within the range of the defenses to drop the team within three miles of the target without taking any flak fire.