These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
At the United States Navy Strike Fighter Tactics Instructor program (formerly known as TOPGUN) today, anyone on staff who quotes or references this movie gets fined $5.
Anyone caught singing "Danger Zone" while piloting a Tomcat, supposedly, is considered a hostile. It's hopefully all a joke, but ejected pilots who sing "Take My Breath Away" are to be shot at. Considering the F-14 has been retired from service due to wear on the airframe, it's likely moot at this point.
Ho Yay: Put it this way; when the studio saw the initial cut, they made the film-makers call Cruise and McGillis back to shoot extra scenes, as the romance between Maverick and Charlie seemed so perfunctory compared to Maverick's "friendship" with Goose. Even in the finished product it's rather blatant — "I'm gonna have somebody's butt for this!", the volleyball scene, "You can be my wingman any time...", "This stuff gives me a hard-on."/"Don't tease me."
Even in the final version, Tom Cruise arguably has far more chemistry with Val Kilmer and Anthony Edwards than he does with McGillis.
Values Dissonance: Although this movie is today often seen as a flying movie that remains a Cult Classic among pilots and aviation enthusiasts, enjoyed for its Eightiesnostalgia value, or else enjoyed ironically for its (arguably) unintentional Ho Yay, when it was first released in the U.S. it was a wildly successful mainstream blockbuster. In Japan, however, it was almost immediately branded a "gay" movie for the very reasons that attract its Ho Yay following and is rarely viewed as anything else even today, possibly due to the choice of voice actors.