Continuity mistake: When "Charlie" is first introduced to the class, she struts down the aisle in heels. When she follows Maverick into the building, you can briefly see that she is wearing flats to compensate for Maverick's short stature. (00:26:00 - 00:28:50)
Other 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.
Continuity mistake: When Maverick leaves Charlie's house after their first date, there is a "For Rent" sign in front of her house, but it's not there when he arrived for the dinner date. It appears to be the same shot of Maverick leaving her house towards the end of the film, when she's actually put the "For Rent" sign up and moved. (00:43:00 - 00:48:03)
Visible crew/equipment: When they return to Enterprise after their successful mission, Iceman points and shouts, "You!" at Maverick. In the shot facing Maverick as he turns his head, the reflections of the camera and large reflector screen are visible on Maverick's sunglasses. Also, note the lack of a crowd of people behind Ice in the reflection. (01:40:45)
Visible crew/equipment: During Cougar's standoff with the MiG, Maverick comes in to assist him. Right after he says "I'm on my way" a few cuts happen then we see the right (or starboard in the Navy) of Maverick and Goose's F-14 along with the canopy. A camera can be seen in front of the copilot, onto of his instrument console.
Suggested correction: It could be argued that in the alternate reality of Top Gun the fictional "MiG-28" was an improved reverse-engineered F-5 (VPAF gave the Soviets access to ex-VNAF F-5:s for evaluation after the fall of Saigon) explaining their similarity.
This isn't a valid correction for a trivia entry. There is no mistake being suggested, just letting viewers with limited plane experience know MiG-28 isn't a real plane.
Bishop73