Filmmakers might not know that navy fliers are not called "Navy pilots", but rather "naval aviators", as seen in some of the between-scene titling. This is a distinction of great dignity to naval aviators who see themselves better fliers than other branch "pilots".
During Jay's F-14 dogfight with the F-5 "Saint", the exterior shots are clearly of an F-14 Tomcat, but when footage is shown of Jay's face and torso from inside the cockpit, the unmistakable wings and outwardly canted vertical stabilizers of an F/A-18 Hornet are plainly visible through the canopy behind him. This mistake is repeated again while Jay is attempting his first carrier landing. When the camera is on Jay in the cockpit, it's obvious that he is once again flying in an F/A-18 Hornet, but exterior footage from the carrier shows an F-14 Tomcat landing on the deck.