Soldiers of African heritage were not integrated with Caucasian units during World War II. This did not happen until July 26, 1948 when President Harry S. Truman signed Executive Order 9981, ending segregation in the armed forces, and not fully enforced until Secretary of Defense Robert S. McNamara issued Directive 5120.36 fifteen years later on July 26, 1963.
The C47's that are carrying the 101st Airborne supposedly have left around midnight. Yet when they are crossing the English Channel, it appears to be early dawn. When they are crossing over the coast of France, though, it becomes night again.
Early in the movie when Boyce is struggling to get loose from his parachute and swim the the surface of the lake he cuts the lines with his bayonet. As he swims to the surface there isn't anything in his hands, but when he gets to the surface he again has the bayonet and uses it to cut a hole in the parachute.
At 1:20h into the movie, we see the German radio room in detail. All the radio equipment visible there is indeed of WWII vintage. But the problem is - NONE of it is German, it is of American and British manufacture. What we can see on those shelves: AN RCA AR-88 receiver (USA); a Collins Navy TCS-12 receiver (USA); a National HRO receiver (USA) and a British R-1155 receiver, the latter used only in Lancaster bomber aircraft.
When the airborne trooper free falls 30 seconds before opening his parachute, he would have impacted the ground much sooner. D-day drops were made at 700 feet AGL, which didn't allow time for free fall and required the static line to deploy the parachute immediately. As reference, the first 10 seconds of free fall take ~1000 feet. The idea of dropping at lower altitudes is to not give enemy gunners much time to shoot paratroopers under canopy.
The only African-American airborne outfit was the 555th Parachute Infantry Battalion (Triple Nickels). Although the unit was ready for combat, it came close to being used in the Battle of the Bulge but that crisis passed and the unit never went overseas or saw combat.
The racial attitudes in the films reflect the 21st century, not 1944. Not only would African American soldiers not be in the White military units, many White soldiers at the time wouldn't even talk with or to them. Additionally, there would be a great more racial epithets spoken than were during the film.
Paul, an 8-year-old boy in a small French village in 1944, owns a baseball glove and ball. Before the end of WWII, nobody in France played baseball, and gear was impossible to find, even in peace time. Even in the 21st century, baseball remains almost unknown in France, being only played at an amateur level by a small group of enthusiasts or Japanese expats. No TV channel shows games, there are no baseball fields or parks anywhere and no mainstream retailers carry the gear.
On June 6, 1944 the Allies sent the paratroopers between 6am and 7am. In the wee small hours of the morning in June, it's already pretty much daylight. Yet, the sun rises only after a good hour into the movie.
The U.S. Army soldiers are incorrectly wearing the colorful Airborne shoulder patches (white eagle head, yellow beak, red tongue), rather than the drab, green and black "subdued" patches worn in combat. (See Saundersinsignia webpage for a comparison). Either the screenwriters weren't aware of this difference or perhaps thought that film-goers wouldn't notice or be more impressed seeing the colorful version which is worn on uniforms for non-combat events such as parades, etc.
The flashlights used by the Amrican soldiers are extremely bright. They appear to be L.E.D. (light emitting diodes), with a high lumens beam. These were not available until at least 50 to 60 years after WWII. This is obviously a revealing mistake.
The goof item below may give away important plot points.
At around the 51 minute mark, when Boyce pulls back a curtain revealing a woman's head solely attached to a spine with no other organs. The head repeatedly says "Stop, please" in French. Even if a disembodied head could be thus reanimated, it would be impossible for it to have a voice without lungs.