Continuity mistake: In the opening scene, as Lasky prepares to board the helicopter, a blue GM station wagon is seen in the background, parked in front of a yellow Pinto. Watch carefully, as the car is partially hidden by the limo. By the last shot, the station wagon turns into a Ford sedan. (00:02:20 - 00:03:25)
Continuity mistake: A helicopter ferries Lasky to the Nimitz, but as it takes off, it is marked as unit 9010, but in flight after passing the Arizona Memorial, it is unit 9717. (00:03:30 - 00:04:30)
Continuity mistake: As the helicopter lands on the USS Nimitz, there is no number on the nose. But as Lasky disembarks, the number "3" appears. (00:06:25)
Continuity mistake: When Lasky heads toward the conning tower, an A-7 Corsair is shown at left (and the helicopter nose has a number "3" on it). As he is led inside the tower, the camera pans up, and now the Corsair is gone, replaced by an E-2 Hawkeye (and the number "3" on the heli is gone, too). (00:06:45)
Continuity mistake: At the beginning of the movie, Cmdr Owens lands an F-14, number 200. Immediately after landing while the plane is raising its tail hook, we see the number 203 on the right wing flap, then after a short cutaway, we see the plane again taxi to the right but now the right wing flap's number is back to 200. (00:08:35)
Continuity mistake: There are two F-14s that deal with the yacht and the two Zeros. They are respectively numbered 202 and 203 prominently on both sides of their forward fuselages. But when one fires a missile to down the second Zero, suddenly it is number 200, a jet that hasn't been launched. (00:50:25)
Continuity mistake: The yacht has been blown up by the Japanese Zeros. A helicopter is sent out from the USS Nimitz to pick up the survivors. When Charlie (the dog) is being lifted into the helicopter (carried by Commander Owens) he is obviously soaking wet. When Commander Owens hands Charlie over to Laurel, Charlie is suddenly bone dry. (00:54:05)
Continuity mistake: During the dogfight with the Japanese Zeroes, the ordnance hung on the two F-14s' weapon stations keep changing. For the weapons to change, the airplanes would have had to land and re-arm about four times during the two-minute dogfight.
Continuity mistake: When the Japanese pilot arrives on the Nimitz after being pulled from the water, he is bone dry as he gets out of the helicopter.
Continuity mistake: Weapons come and go in the battle scene between the two F-14's and two Zero's. One of the F-14, supposedly 203 but marked 200, fires a sidewinder from its left side and the hard point is completely empty, it was fully loaded at the start of the combat and had only fired 1 missile. The AIM-7 Sparrow which was supposed to be there is gone, also all the AIM-54 Phoenixes that were seen earlier are gone as well. In the next shot showing 202 and 203 flying next to each other, both planes are fully loaded again, no missiles fired at all.
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.