The first shot of John McClane in Die Hard is his left hand digging into the armrest as his plane lands at LAX. We can see he’s wearing a wedding band on his ring finger. His seatmate then gives him an unusual piece of advice about surviving air travel: once he settles in, he should take off his socks and shoes and make fists with his toes on the rug. Then he reaches up to the overhead bin, revealing a holstered gun dangling from his midsection.

All of this is mundane stuff. It’s also a prime example of why Die Hard remains the greatest American action movie since it was released 30 years ago this week.

Consider everything that the director, John McTiernan, and his screenwriters, Jeb Stuart and Steven E de Souza, set up in this brief little scene. Though Bruce Willis plays McClane as the modern American cowboy, Roy Rogers with an attitude, the film-makers choose to emphasize his vulnerability first. His fear of flying gets us primed for the bumps and bruises he will sustain all night long, when a phalanx of terrorists take over a Christmas party at Nakatomi Plaza. McClane’s most important quality isn’t his toughness, but his flesh-and-blood humanity, which is what most of the film’s sequels get wrong. The advice he gets from his seatmate gives him a reason to be barefoot during the entire ordeal, including a sequence where henchmen deliberately shoot out the glass to shred his flat soles. The gun establishes him as one of New York’s finest, and the ring suggests a commitment to his marriage that his wife Holly (Bonnie Bedelia), we soon learn, doesn’t share.

There are dozens of other examples of small, deftly planted details that will pay off later on. The first terrorist McClane kills has feet “smaller than [his] sister’s”, so he can’t take his shoes; he also happens to be the brother of Karl (Alexander Godunov), the vicious right-hand to the mastermind, Hans Gruber (Alan Rickman), which raises the stakes for their inevitable mano a mano. And that famous shot of Hans falling to his death from an upper floor after McClane unclasps the watch from his wife’s wrist? That Rolex is accounted for, too, in the early going, when it’s revealed to have been a reward for Holly’s excellent performance for the company. The watch is a painful symbol of their separation, because she left New York to pursue her career ambition and he didn’t follow. Unclasping the watch means more than merely saving her from peril.

There’s not a wasted moment in Die Hard, not a moment when the audience feels confused about who’s who or what’s going on or where the characters are in relation to each other. It seems like simplest, most banal part of a making a movie, but it must be the hardest, because the vast majority of actioners, even good ones, don’t succeed in doing it. Stuart and De Souza’s script is a perfectly worked-out puzzle of a thousand tiny pieces: Die Hard has at least five major villains, unfolds over multiple planes of action, and fully works out Gruber’s elaborate scheme to steal $640m in negotiable bearer bonds (he’s no mere common thief, he’s an exceptional thief) and McClane’s improvised efforts to stop it. “I always enjoyed to make models when I was a boy,” says Gruber at one point, in the meticulously jumbled English of a native German. “The exactness, the attention to every conceivable detail.” This is the screenwriters showing a little swagger.

Photograph: Alamy Stock Photo

In the decade that followed, Die Hard served as the template of the modern action movie, to where “Die Hard on a …” would become its own subgenre: Die Hard on a bus (Speed), Die Hard on a ship (Speed 2: Cruise Control, Under Siege), Die Hard on an airplane (Passenger 57, Executive Decision), Die Hard on an ice cream truck that must stay under 50 degrees Fahrenheit at all times (Chill Factor). The dominant location, the everyman hero, the colorful terrorist – some of them got one or two elements of the formula right, others were chintzy facsimiles, but none felt as satisfyingly complete. Once Michael Bay made The Rock – Die Hard at Alcatraz – the entire language of action movies started to shift into a more visceral rush of images, sensation without context. And the rise of CGI in The Matrix and onward, with its infinite plasticity, made the physical action in Die Hard even more a thing of the past. (The evolution – or devolution – of the form can be tracked in the Die Hard sequels, which eventually turn McClane into superhero without the cape and spandex.)

It’s strange to think of Die Hard as a stodgy old classic, but it has been 30 years since it opened midsummer and dominated the back half of 1988. To put that in perspective, Alfred Hitchcock’s Vertigo, Orson Welles’ Touch of Evil and Akira Kurosawa’s The Hidden Fortress were released 30 years before Die Hard, and the distance between eras feels even more profound. (Die Hard itself has a joke on the subject, when the two FBI guys circle the building in a helicopter: “Just like Saigon, eh, slick?” “I was in junior high, dickhead.”) And as with any classic, repeat viewings call attention to grace notes and trivial bits of business, like the hat tips to other movies (the head of Nakatomi is named Mr Ozu and “the seventh seal” opens the vault) or the savage parody of live TV coverage, in which a talking head blathers on about his book Hostage Terrorist, Terrorist Hostage: A Study in Duality.

All the canonical moments and lines still play: McClane crawling through the air duct or leaping off the exploding roof with the firehose wrapped around his waist, any of Alan Rickman’s archly enunciated monologues: “We’re gonna need some more FBI guys, I guess”, “Yippie ki-yay, motherfucker”. The lesson of Die Hard, however, is that the small, incidental details are just as consequential – and often exactly what’s missing from the films that tried to emulate it.