Factual error: Captain Bernard Rawlings, the British naval attaché in Tokyo at the beginning of the film, wears no medal ribbons. In fact, as depicted in photographs, Rawlings would have had several ribbons by that stage, including First World War service ribbons and the OBE he was awarded in 1920.
Factual error: Rear Admiral Raymond Spruance is the tactical commander during the Battle of Midway in the film when in reality it was Vice Admiral Frank Fletcher who was in charge.
Suggested correction: While true it's not a mistake, as the movie deliberately focuses on Spruance because of his greater role in the actual battle. Spruance was on scene approximately 36 hours before Fletcher. He had two carriers to Fletcher's one. After Yorktown was torpedoed, Fletcher evacuated to a nearby cruiser. When Spruance asked if Fletcher had additional orders, Fletcher replied "will conform to your movements", effectively turning command over to Spruance.
They didn't 'focus' on Spruance. They deleted Fletcher.
Semantics. If Fletcher is deleted, the only USN Task Force Commander left for the movie to focus on is Spruance.
Continuity mistake: The ack-ack Japanese gunners seem to be the same 2 on numerous ships and carriers. One grits his teeth and the other has a long concentrated look.
Factual error: They show several scenes of Pearl Harbor after the attack where there is no indication that anyone is observing blackout regulations when in reality the whole island was under blackout conditions afterwards.