Plot hole: Danny receives the telegram from Rafe, telling him that he is alive, at the same time Rafe meets with Evelyn. The telegram must have been sent from Hawaii. Why didn't he just call on the phone? When Rafe reached the U.S. after leaving England why didn't he send a telegram then. In those days it took some time to travel from the Eastern U.S. all the way to Hawaii and there is no way he beat the telegram if it was sent when he returned to the U.S.
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.
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.