Continuity mistake: In the scene where Danny, Rafe and Jimmy Doolittle are on the deck of the Hornet talking about "returning" the friendship medals before the attack on Tokyo, you can see what appears to be a radar dish covered with a grey tarpaulin. The scene cuts back to Doolittle, Danny and Rafe talking some more, and then back to a wide shot of Doolittle walking away. The mysterious tarped object is completely gone now.
Continuity mistake: When Rafe and Evelyn go to the Queen Mary ship and they are rising on the platform, and kissing, one sweeping camera shot shows the handle of the elevator controls going straight up. This would mean that they had stopped, yet they are still moving up. A couple of seconds later, a close up of the handle shows that it is now in the position to move the elevator up.
Plot hole: In the scene where Danny and Evelyn are talking, Danny 'finds out' that Rafe volunteered to go to England. Danny already knew that Rafe volunteered because near the start of the film, Danny was in the same office as Rafe when Rafe was given the choice to go to England or not.
Continuity mistake: When we see the Navy Department's "vacant sea map", there is a guy holding a cane and explaining what it means. He walks around the globe in the middle of the room holding onto the side of the globe with his left hand, but in the following shot his left hand is on the cane. (01:05:05)
Continuity mistake: In the scene where Rafe is burning his love letters on the beach after learning Evelyn is pregnant with Danny's child, when Danny and Rafe are talking there is a modern "dune fence" meant to keep people from walking on sensitive dune plants clearly visible in the background.
Continuity mistake: In another scene when Danny and Evelyn are at the Black Cat diner after leaving the cinema she gets up to leave first, but when she gets up there is no hankie on the table. After the camera shows her walking out the door, it cuts back to Danny who picks up the hankie, which was not there a second ago. (00:55:10)
Continuity mistake: When Rafe is taking Evelyn to the boat in the beginning of the movie to sit on the lighted platform, they clearly pass the same platform about 2 or 3 times before they get onto it.
Factual error: As the Japanese fleet steams toward its launch point, there is a close up of the nose of a B5N1 Kate torpedo bomber with its distinctive two-bladed propeller. Trouble is, the Kates used against Pearl Harbor were B5N2's, with a two row radial and 3-bladed prop.
Factual error: During the Air raid scramble of the RAF squadron, one pilot behind the RAF mechanic can be seen to be boarding a Hawker Hurricane, not a Spitfire. As far as I am aware, Hurricanes and Spitfires were never operated in mixed units. Squadrons had one or the other.
Continuity mistake: When one of the Men are speaking to the President about the boys having to take the airplanes off the carrier too soon, you can see there's a ring on his left pinky finger, but no wedding ring.
Factual error: When the raiders are just over their targets, the pilots of the flights order bombs away and the bombs immediately drop. The problem with this is it's the bombardiers job to decide when to drop the bombs on the target. If the pilot dropped the bombs, you wouldn't need the bombardier or the bomb sight.
Factual error: In January, 1942, US National insignia deleted the red ball in the center of the star. The Doolittle raiders are depicted with the old insignia, and while this was accurate on the fuselage and wing bottom, official US Navy photographs show that at least some of the B-25's had the newer insignia on the top left wing.
Factual error: When Rafe comes to England he gets a damaged Spitfire to counter the Luftwaffe. If you ignore the fact that he should at least make some flying hours in a Spit before going into combat, no one had to fly a shot-up Spit during the Battle of Britain, since Spitfire production could quite well keep up with the war losses. It was lack of fighter pilots that almost caused Britain's defeat.
Factual error: The scenes of fighter planes chasing each other are fanciful. The planes would never be so low (they look like thay're only ten feet off the ground), much less weaving between hangar buildings and warehouses at 250 mph. That kind of flying is impossible. Other similar shots, showing Japanese fighters flying between the masts of battleships, are equally unrealistic.
Continuity mistake: At the start of the attack, the Japanese fly past a baseball court with some kids playing baseball. In one shot we see perhaps two or three kids in the batting cage. If you look to the far left you can see a woman. In the following shot she is now suddenly where the batter was. (01:23:10)
Continuity mistake: When Rafe and Evelyn go to the Queen Mary and are rising on the boat is one sweeping camera shot. Look to the right as their boat goes up and you can see the film crew going up on a platform. Note that the next shot of them on the boat is filmed from that platform.
Plot hole: Near the end of the Tokyo raid, Col. Doolittle orders his radio operator to "break radio silence" so he can address the rest of the planes. For the duration of the raid, though, intelligence officers had been listening to radio transmissions back at Pearl (other users have already commented that this in itself is a historical error). If these transmissions were being heard at Pearl, there was obviously no radio silence to begin with.