Revealing mistake: When the Marines shoot the Japanese pilot, you can see the wire used to set off the blood bags coming out of his pants leg as he falls. (01:11:30)
Revealing mistake: When the Zeros destroy the yacht, mooring lines can be seen holding the boat in place as it explodes. Obviously, it isn't actually at sea, but is very near shore. (00:45:35)
Revealing mistake: During the dogfight scenes, they show the pilots of the F-14. In the visor, you can see the reflection of an A-6 instead of an F-14 being used. Turns out, they dressed up some A-6 aviators as F-14 aviators for the shots.
Answer: Apparently, the storm that pulls the carrier to another time can also catch planes in flight. It caught the planes launched to intercept the Japanese attack, and pulled them back to the future along with the carrier.