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.
Character mistake: In the opening scene is a paragraph describing why the Top Gun school was started. The word "insure" is used when the word should have been "ensure". They wanted to guarantee the U.S. had superior pilots, not take out an insurance policy.imshiffman
Continuity mistake: Take notice of everyone's hands during the action sequences. No one is wearing gloves. As standard issue for military pilots, the gloves are made of Nomex and provide protection from fire and allow for a better grip when things get a little hot and heavy.
Other mistake: Charlie is chasing Maverick in her car to tell him how she feels. Maverick races down the road on his motorcycle, then two cars start to move out of an intersecting road and Charlie narrowly misses them. In the next shot, Maverick starts yelling at Charlie about her 'reckless' driving, but behind them, you see the highway, with no traffic lights or signals. Charlie actually had right of way.
Factual error: The training was conducted at Miramar, 5 (or so) miles from the beach. When Charlie confronts Maverick about his flying and he leaves on a motorcycle, he zooms up a hill away from the ocean leaving NTC SD (Naval Training Center San Diego - not Miramar) with the Coronado Bay Bridge - and lots of ocean water - in the background.