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.
Complete Monster: Hans Gruber, the villain of the first movie, is definitely a Complete Monster. While he seems to be accommodating towards the needs of the hostages after they're addressed to him (providing a sofa for a 9-months pregnant woman, for instance), he actually is intending to kill every single one of them to cover his escape by herding them onto the roof, then blowing it up with a massive amount of C4 when the helicopters get near.
Colonel Stuart of Die Harder, who murders a plane full of innocent peoplejust to make a point that his demands and threats are serious.
The only main villain to subvert this is the one from With A Vengeance, Simon Gruber. He calls the NYPD to say that he's planted a time bomb in a New York City elementary school, but he leaves only a vague clue as to its location. He does this to divert police attention away from his actual target; once the bomb is found and revealed as a fake, he tells McClane, "I'm a soldier,not a monster. Even though I sometimes work for monsters."
Thomas Gabriel is willing to crash the entire nation (not to mention the planet considering how interconnected we all are) for both his revenge and his greed.
Crazy Awesome: McClane takes out choppers with cars, swings in via fire hoses and takes on a whole building of terrorists barefoot in a wifebeater. And destroys a multi-million dollar jet fighter, though that was mostly by accident.
Critical Research Failure: Die Harder: Aviation doesn't work that way. At all. In fact, Airplane! is probably more accurate. The villains' plan involves shutting down air traffic control at Washington Dulles International Airport so as to prevent interference with their plot. This creates drama via the fact that a lot of planes are unable to be given instructions to land at the airport, so they're all circling the airport with dwindling fuel supplies. There's just one problem: FAA regulations state that all passenger airline flights must carry enough fuel to divert to another major airport close by in case of an emergency, like the one depicted in the film. The film takes place in Washington D.C. There is a second major airport in DC (Ronald Reagan Washington National Airport) and a third if you count Andrews Air Force Base, which is more than capable of landing civilian airliners, as it is the home base of the President's 747. Furthermore, Baltimore is close by and Newark, Philadelphia and New York City (two major airports in the city) aren't a terribly long distance away either. In short, the suspense of the movie never should have happened.
Evil Is Sexy: Maggie Q's character in Live Free or Die Hard, which McClane comments on.
"That girl of yours? Smokin' hot."
Her boyfriend, Thomas Gabriel (played by Timothy Olyphant), is quite easy on the eyes himself.
This trope is pretty much a given when your villain is being played by Alan Rickman.
And then in With A Vengeance, he has to stop a bomber from exploding a bomb on a subway. It would seem Speed is even more like Die Hard (On A Bus and Subway Train) than first supposed.
Harsher in Hindsight: In Live Free or Die Hard, the Big Bad's apparent motivation for messing with America's computer infrastructure is to teach them a lesson for ignoring him about the threats cyberterrorist can pose. In Real Life, Dr. Bruce Edward Ivins was suspected to have caused the 2001 Anthrax attacks for this same reason.
In With A Vengeance one of the cops makes an offhand comment to the 1993 bombing of the World Trade Center, and how darned inconvenient it was. Ouch.
Looking at the first three films: a tower gets blown up, a terrorist plot with airplanes, and New York City in danger.
In the first film, Sgt. Al Powell is ashamed of himself after he shot a kid because he mistakenly believed he had a gun. In 2012, after the shooting of teenager Trayvon Martin, it was initially believed that George Zimmerman, his shooter, shot him because he mistook his Skittles bag for a gun.
It Was His Sled: Most of the films. Yes, including the 4th. Yes, even on this very website, which makes it very difficult to watch the entire series unspoiled.
Magnificent Bastard: Hans Gruber, especially when he gets caught at gunpoint by McClane and almost gets away with simply using an American accent to pretend to be a civilian. And even then, after his henchmen turn up, he manages to do some serious damage to McClane by taking advantage of his bare feet and shooting the glass.
Strawman Has a Point: Gabriel did try to warn the government who hired him that their security was woefully inadequate... It still doesn't stop him from exploiting those weaknesses to get rich and kill people (and not in that particular order).
Weird Al Effect: Everybody knows McClane's catchphrase "Yippie-Kai-Yay, motherfucker!", but few now remember that the line (or at least the "Yippie-Kai-Yay" part) was derived from the western song "Git Along, Little Dogies".