When Crosby is leaving the restaurant, he has captain rank visible on his shoulders, but when he arrives at the hotel room he is wearing major rank insignia.
While it is true that the actual Harry Crosby slept through the D-Day invasion, in reality he only slept for a full single day, not the three the episode depicted. Also, he did not collapse in the main operations room as was also depicted. Instead, he drove back to his barracks in his jeep, and on the way almost hit a tree due to his extreme fatigue.
While briefing the 99th Pursuit Squadron, the men respond to the commander twice by saying "Sir, yes sir!"
That response is used by the US Navy and USMC, not by the US Army. In the army, the response is "Yes sir!".
Colonel Davis said, "Ceiling and vision unlimited." The correct words for CAVU is Ceiling And Visibility Unlimited.
The officers cheer when they learn about the upcoming invasion of Europe. However, according to the titles, the briefing occurs on June 6. The D-Day landings had to be postponed for a day due to bad weather, so by that day they should have known about Operation Overlord.
The Red Tails are shown bombing a target low level. They are so low and close to the target that they barely clear it. In real life no pilot in his right mind would ever attack a target from such a low altitude, since the explosions from his own bombs would likely cause him to lose control of his aircraft. This is a well-known fact among military pilots... at least, the ones who survived.
On June 3, 1944, Crosby, as narrator, said that it was three days before D-Day. D-Day was scheduled for June 5. It wasn't until June 4 that Eisenhower postponed D-Day for 24 hours because of bad weather. However, Crosby acts as an omniscient narrator. He is speaking after the war about events that he lived and many stories that he did not witness. Therefore, he knows that D-Day would actually begin in June 6.