I've enjoyed this film in the theater and on TV and recently acquired it on DVD. One of the nice extras is a commentary track by the film's director of photography. He provides fascinating details about the actual shooting such as the fact that all the shipboard scenes were filmed on board the Nimitz during a brief layover and a week-long training exercise. The technical aspects of the DVD are well done.
Some story elements may have been overlooked or perhaps altered in the editing. The Nimitz' strategic policy was initially nonintervention and self-preservation. The F-14's were ordered to shoot down the Zeros, not in reprisal for their attack on the yacht, but in order to stop them from finding the carrier with its armament-laden deck. The decision to engage the invading force came about only when attack was imminent. When the captain learned that the time vortex was actively pursuing the ship and escape was impossible, he recalled his men in order to avoid stranding them in time. The only time-altering consequence of the whole scenario was to deposit Commander Owens in a situation where he could affect the future. The reason for that action and the nature of the intelligence behind it is left to the imagination.
If you enjoyed Final Countdown, check out the recent anime series Zipang. It's an alternate telling and role-reversal of this story. A modern Aegis vessel from the Japanese Self Defense Force is transported back to the Battle of Midway and presented with the opportunity to alter the outcome of that engagement. It's a well told story with realistic animation, unlike typical Saturday morning action cartoons.