Revealing mistake: After Danny's plane crash lands in China, and Rafe runs towards the crash site, he shoots a Japanese soldier. After his next to last shot, the slide locks back on his pistol, indicating it is empty. You can see the slide locked back moments before he takes his last shot, with an empty gun.
Continuity mistake: When Doolittle's raiders are first starting to practice short takeoffs, the flaps of the planes aren't extended in close ups but would have to be for takeoff especially short takeoffs. Planes shown taking off have the flaps extended. In the real takeoff from The Hornet, One pilot retracted his flaps because prop wash from previous planes was lifting his plane. He then forgot about it and took off without flaps extended and was only saved by the heavy wind and forward speed of the carrier. There is actual video of the plane nearly hitting the ocean.
Factual error: In the RAF squadron scene, the lined up Spitfires are the wrong mark for the period. For early 1941, the correct mark would have been a mark V. The Spitfires are later, as they have six exhaust outlets per side, and several have four-bladed propellers, neither feature being present on mark V Spitfires.
Continuity mistake: When launching Doolittle's plane from the carrier the deck is smooth. When Rafe's plane launches the deck has catapults. The following planes are back to smooth decks with no catapults.