Every line in the movie adds to the film. Nothing is wasted. And if there is something, I can't see it. Yes, there's a reason I'm not breaking this up, mainly the dialogue feeds into both the character and the plot ... and because character adds an extra dynamic to this plot.
The first scene alone does so much, it's stupid. Remember, the scene is John McClane talking to the passenger next to him on an airplane. It gives him a reason to be shoeless during the movie, and establishes his profession, and is already adding to his character by both giving us his CV in a smooth, effortless way. It establishes his anxiety about flying, giving him a cute character trait. Also, it already shows us just how much of a smartass he can be... McClane's shoeless wardrobe "choice" in the film leads into a brilliant, brilliant moment that deeply hurts him later on.
We've already covered how the Rolex adds to the plot, and that was all covered in three lines of dialogue -- it both underscores Ellis' pursuit of Holly, struts it before John McClane, and dangles this metaphorical gun in front of the audience's face without anyone realizing how integral ANY of it actually is. Ellis, who has few lines in the movie, serves many functions. One, his presence gives a counterpoint to McClane's actions throughout the film -- no matter how many gunman McClane takes out, he's still only one person. Ellis is one of the many realists in this film, but the only one who is among the hostages.
Ellis' strutting egomania, his coke problem, and his focus on Holly all culminates in the pinnacle of his arc. His egomania and his drug problem drive him to try and negotiate with Hans and company -- he thinks he can talk them down, give them what they want, and they can all go home. And while he gives them McClane's name and occupation, Ellis makes it a point to spin the story that he brought McClane to the party, and there is no mention of Holly. For such a minor character, Ellis provides a lot.... even though giving up John's name will eventually lead to Holly. And his death is one of the few things that hurts McClane.
And that's a secondary character. Maybe even tertiary.
Dialogue establishes a lot in this movie. It establishes Mr. Takagi's character and backstory with Hans' first speech, and adds an emotional blow to Takagi's death. The offhand lines about needing the FBI, and "it's all part of the plan" feed into the turning point of the film, and a mystery that is on par with any twist by Mission: Impossible, Leverage, or Jeffery Deaver. In fact, I would say that Deaver was warped by Die Hard.
A lot of things in the second half of this movie are almost perfect mirrors to stuff from the first half. The conversation between John and Holly in (what I think is) her private bathroom leads directly to a conversation that is the turning point of the film... which is also in a bathroom. McClane is at his lowest point. He's been wounded physically and emotionally. It's the flip side of the earlier conversation with Holly, and while it's depressing, it has a point, and also accomplishes much. McClane's relationship with the LAPD Sgt. Powell, outside of the building comes to a head, and it leads directly to the punchline.