At the beginning when Hardison is telling them about Lawson Sophies's hands change position between camera angles.
The sniper that attacks the squad is firing far too fast for a Mauser 98k. That weapon is a bolt action, not a semi-automatic. If he was firing at the rate the sound effects suggest, he would not have time to even aim the rifle between shots.
That "supply" troops, specifically african-americans, would be unarmed is incorrect -- all troops in a combat area were armed. That a truck would somehow be the centerpiece of a patrol searching for a sniper is also incorrect, that the driver of a truck (white or black) in a combat zone would be unarmed is silly.
"It is not the policy of the United States Government to hand out medals to negros" is incorrect (and a trifle insulting to the viewer.) While medals of honor were hard to come by for African Americans, they were awarded many other medals in WWI and WWII, including Distinguished Service Crosses (second-highest award for bravery), silver and bronze stars, and awarded at the time of the combat, for instance in 1918 (wwi), 1944 and 1945. African-American soldiers were brave and risked their lives in combat to serve their country, and the fable woven by this episode is simply not true -- and only cynically used by the makers to "justify" the theft by Charlie.
Charlie Lawson says they landed at Calais after D Day. While this is possible, Calais was not liberated until November 1944 by the Canadians. Only personnel were able to be landed through this port. However, Calais was within the UK army's entry points and it is highly unlikely a US supply unit that Charlie was with would have landed there.
"There weren't a lot of choices for a black man in the army", says Charlie. The implication, that African-Americans were only allowed to be truck drivers, and not fight, is incorrect. For instance, the 99th Fighter Squadron (trained at Tuskeegee), the 477th Bombardment Group, the 761st Tank battalion, the 92nd infantry division, and many other units.
The tent seen at 19:47 is a standard late 1970's (and later) U.S. military aluminum framed, nylon fabric covered tent, used during the first Gulf War (in which this contributor served). A tent from the WW II period would have been a GP Medium Tent framed with wooden poles and covered with canvas waterproofed by the era's methods.
When Elliot is trying to con his way into the house as a Gas Company inspector, he states that the gas detect is at 84% LOL. The correct term would be LEL for lower explosive limit. Given Elliot's background, he should be familiar with the correct term.