Continuity mistake: Throughout the film Maverick's plane has the number "114" on it. However, at the end when he is waiting on deck, the number has changed to "104". This is actually Iceman's plane, which has already taken off. When Maverick launches, the number has changed back to "114" again.
Revealing mistake: In every in-flight cockpit scene a brass hand wheel is visible on the right side of the headbox of the seat. The only time this hand-wheel is installed on the seat is to disconnect the seat from the aircraft and to disarm the seat. Therefore, the plane and actors in those scenes were on the ground with a moving camera because there is no way that an F-14 would be allowed to fly with "dry" seats.
Continuity mistake: When we are first introduced to Maverick and Goose, their Tomcat crosses the screen, right to left, in close-up, slowly. It's nose is marked 203. Then we see the other Tomcat flying with them, and it is number 114, and its crew is Cougar and Merlin. But all the shots after this place Maverick and Goose in 114.
Visible crew/equipment: In the scene after Maverick and Goose were told that they would be going to Top Gun the next scene shows Maverick on the runway riding his motorcycle as planes fly by. If you have your DVD settings on full screen you won't notice this but on wide screen you will. You can see the motorcycle that he is riding is strapped down to a trailer with 2 blue tie-down straps. Also, if you listen and watch closely you can tell that Maverick is not shifting and giving gas to the motorcycle at the right time. The only reason I know this is because I have been riding for over 10 years. If you give a sport-bike like that gas, it goes. He gave gas and it never even moves on the screen. Hard to do when you are strapped down to a trailer.
Factual error: In all sequences where Maverick "puts on the brakes", he is shown pushing the throttle quadrant forward and pulling the stick back. This would put him in a full-afterburner climb, but you don't really stop and it doesn't work in a medium speed tail chase (which is easier to film). The air brake does effectively nothing on the F-14 because it is too small, and not deployable at full power.