Other mistake: In the Darkstar takeoff sequence, there is a cockpit shot where Maverick looks back after passing over the Admiral, then looks forward into the cockpit. You can see that the landing gear handle is still in the "down" position and the 3 "gear down and locked" lights are illuminated. At this point in the flight the gear has already been retracted (confirmed visually in the previous external shot).
Other mistake: When Cyclone and Warlock show Maverick the 12 candidates, Maverick looks at Rooster's profile, left of which is that of Hangman. There you see that Rooster and Hangman have the same Department of Defense ID: 720,956,349. (00:20:06)
Other mistake: The beginning footage shows the USS Roosevelt CVN 71 as the carrier being used for flight ops, yet they refer to it in the movie as the USS Lincoln, CVN 72.
Suggested correction: You are absolutely correct, except it's never suggested they are the same aircraft carrier. The opening sequence is just for "flavor."
Other mistake: After Hangman shoots down the last 5th Gen fighter you can see his F-18 in all remaining shots including landing still has all its missiles. (01:55:41 - 01:56:20)
Other mistake: In movie, Harvard and Yale are the crew of one of the dual F18. Harvard is wearing the Navy Aviator Wings on his patch, Yale is wearing WSO wings. Later, in aerial scenes, Yale is in the front seat of the plane and Harvard in the rear - the wrong way round. (01:40:00)