Just prior to Christmas 1944, Tibbets attends a meeting at the White House with President Roosevelt and several high ranking military and civilian figures in which the casualties sustained by American troops during the battle for Naha on Okinawa are mentioned. The Battle of Okinawa did not start until April 1, 1945 and the city of Naha was not captured until some time after Roosevelt's death on April 12, 1945.
When Tibbets is giving his first orientation to the men from the P-38, a C-47 in the background is painted with D-Day invasion stripes. This was only applied to aircraft in the European Theater of Operations so would not have been painted on State-side aircraft.
The bus shown dropping off arriving soldiers at the base is a 1964 model, nearly 20 years out of date for the movie's 1945 setting.
Major Tom Ferebee has to unroll his autographed "Short Shot" money roll to help Colonel Paul Tibbets and himself remember the last name of Theodore "Dutch" van Kirk. In actuality the three men had flown over 40 combat missions together on the same crew in Europe, and it is highly improbable that either Tibbets or Ferebee, let alone both of them, would have forgotten van Kirk's name.
The other pilots refer to Captain Bob Lewis as having been Tibbets' "fair-haired boy on two continents." While Lewis was an experienced test pilot, he had not yet served overseas at that point.