Commander Krennick is seen wearing a hat that is only for Lieutenant Commander and below. Hats for Commander and Captain have "scrambled eggs."
The F-14 is shown running full afterburner in the hanger. This would be extremely dangerous. Only one engine would need to be running, and at idle, to provide power for the avionics.
When the Cubans deny the diplomatic plane clearance to land the Air Force pilot says they have to divert to Miami because that is the closest safe airfield to land at. Which is incorrect, the closest friendly airfield to their location would be Leeward Point Field, the main airstrip for Naval Station Guantanamo Bay. That base has been under the control of the U.S. Navy since 1903 and that airfield has been in service since 1953.