Continuity mistake: In the elevator scene Kelly McGillis's hair is a different colour (I think a shade of red) than earlier or later in the film. Apparently this scene was filmed months after Top Gun filming was complete while McGillis was shooting another film. This explains the baseball cap and ponytail.
Continuity mistake: After the class where they meet Charlie for the first time, and Maverick reveals that he's "the one", he's confronted by Iceman. The Iceman asks him who was watching Cougar, while he was "show boating" with this MiG. If you watch Iceman you'll see that he puts his watch on twice.
Continuity mistake: In the scene where Charlie picked up Maverick from the hospital, you can see the rear view mirror of her car is low, between the actors' faces. The camera zooms in and the mirror can be seen raised slightly above the top of the windshield. The camera zooms out and the mirror is low again.
Continuity mistake: In the beginning scene of the movie, Maverick and Cougar encounter 2 Soviet Migs. When one of the MIgs is first shown from the camera angle on its right side, it is a delta winged aircraft. The next scene that shows the Migs, they have standard wings. The wings change at least twice during the opening air encounter.
Continuity mistake: In the final dogfight, Hollywood and Iceman are up against 5, count them, 5 Migs. Hollywood is shot down and Maverick is launched. Maverick takes out one Mig, Iceman takes out the next. That is two. Maverick takes out a third. For the finale, Maverick hits the brakes and lets him fly right by for a total of FOUR kills. Then the remaining Migs bug out. Two Migs are shown leaving. That adds up to 6 Migs, not 5. [Initially 5 Migs do show up on radar. But just after Maverick launches, Slider tells Iceman "We've got four on our tail. That makes 6 of them". So there isn't actually a continuity error when the remaining two Migs "bug out".]
Continuity mistake: In the scene in the airport after Maverick quits, Charlie tells him, "you've got that maneuver down real well," and it cuts to a close-up of Maverick. Movement is seen in the shiny wall behind him, which is a reflection of Charlie standing up. It cuts to a wide shot of both of them seated. Then she stands up to say, "So long, Pete Mitchell."