Not to mention the way Alan Rickman reads the last part in this incredibly annoyed yet-deadpan manner. "Hoh...Hoh...Hoh."
John McClane dropping one of Hans' henchman's dead body onto Al's cop car just as the latter is getting ready to chalk the call up to a false alarm and leave, and Al's reaction to it, is way, way, way funnier than it should be.
Hans decides to buy time against the police by pretending to have terrorist demands for them. The "demands" he makes are for numerous terrorist prisoners around the world to be released (none of whom have any connection to him), including members of the "Asian Dawn" organization. Karl does a double take:
Karl: *mouthing* Asian Dawn?
Hans: *shrugs* I read about them in Time Magazine.
Karl: "Do you think they will even try to do it?"
Hans: "Who cares?"
"Now I know how a TV dinner feels."
John McClane verbally bitch-slapping the Deputy Chief of Police when he tries to tell him to back off.
Chief: You listen to me, you little asshole, I—
John: Asshole? I'm not the one who just got butt-fucked on national TV, Dwayne! Now you listen to me, jerkoff, you're not part of the solution you're part of the problem. Quit being part of the fucking problem and put the other guy back on!
Argyle was listening on this conversation, laughing.
John: Is the building on fire?
Al: No, but it's gonna need a paint job and a shitload of screen doors.
When the FBI shuts down the electricity to the building, the electromagnetic seal on the vault is lost, and as it opens, Gruber and Theo get looks on their faces that say what they're seeing is beauty incarnate. At that moment, Ode to Joy starts playing.
It's made even better by how (deliberately) preposterously overblown the scene is: a lens flare shines over Gruber's shoulder like the sun rising, and if you look closely, you can see his hair blowing because of a wind machine.
Much of Theo's dialogue. His play-by-play of the police's botched attempt to break into the building is particularly memorable.
"'Twas the night before Christmas, and all through the house, not a creature was stirring, except...the four assholes coming in the rear in standard two-by-two cover formation..."
"Looks like the police have themselves an RV..."
[walking into the building with Karl] "So Kareem rebounds, right? Feeds Worthy on the brake, over to A.C., to Magic, then back to Worthy, right?" [Karl shoots and kills the guard with a shot to the head that is perfectly timed to Theo's speech pause] "BOOM! Two points!"
When the terrorists lock-down the building for the police's initial assault, one of them positions himself in a concession stand to assemble his weapons... and help himself to some candy.
The best bit is how he looks around to make sure nobody's watching first. He's already party to murder, terrorism, and is planning to do a lot more. But it's nicking a Nestle Crunch that he's worried about people seeing.
Even better, this was a Throw It In improv by the actor, who thought that the scene could use some comic relief.
In two scenes, Argyle talks to the teddy bear in the backseat.
(talking to John on his cell, but the connection was cut off by the terrorists) Argyle:(to the bear) You know the number?
(after trying to find a way out, he parks his limo and sighs. He looks at his rear view mirror and sees the bear) Argyle: Shut up.
Special Agent Johnson and Agent Johnson. Note: no relation. Followed later by an unheard but implied question when a caller asks if the black Johnson is the one on the phone. "No, the other one"
More Johnson and Johnson:
Big Johnson: YEEEEEEEHAAAAAAAAA!!! JUST LIKE FUCKIN' SAIGON! Eh, slick? Little Johnson: *smiles* I was in junior high, dickhead.
In a scene near the end of the movie, while McClane is walking through the wreckage of the room where the hostages had been kept for most of the movie, an elevator arrives on the floor, complete with chime, then explodes for no reason.
An apparent throwaway scene has a beautifully condensed Take That against pundits and anchors; The so-called terrorist expert refers to the "Stockholm Syndrome" as the Helsinki Syndrome, the anchor trying to add context "Helsinki, as in Sweden", gets the country right in his mistake, only to be corrected by the expert, "Finland". Cue baffled reactions and facepalms from behind the camera.
Made funnier still in the TV edit, where "asshole" is replaced with "turkey".
Earlier, the moment where two of Stuart's henchmen infiltrate the church dressed as utility workers, and this Pre-Mortem One-Liner:
Custodian: Yeah, I kinda feel like a piece of me is dying along with this church.
Baker: Uh, you're right about that. [pulls out a pistol and shoots the custodian, killing him]
McClane escapes an exploding (parked) plane via ejector seat. The camera remains still and McClane flies towards it. His expression and choice of words ("OH SHIIIIIIIIIIIIIT!") is absolutely priceless.
Especially when McClane tries to get out of the parachute.
McClane: Where's the fucking door?
This exchange between McClane and Major Grant:
McClane: I was wrong about you. I thought you were an asshole. Major Grant: No, You're right. I'm just your kind of asshole.
Made also even funnier on TV, where "asshole" is replaced with "rascal".
Shortly after Esperanza's plane lands, he steps out of the door, proclaiming, "Freedom!" McClane immediately steps in front of him and punches him in the face: "Not yet!"
Not to mention the music.
Holly zapping Dick with a taser on the airplane.
Dick: But at least the truth is not among the hostages because I, Richard Thornberg, just happened to be here to put his life and talent on the line for humanity and country. And if this should be my final broadcast— *gets zapped*
Zeus: You know some kid might come along and find that.
McClane: You're right. (gives him a look)
Zeus: (gives a damn look and grabs it)
And later two of Simon's goons (dressed as cops) are given the bomb by an unknowing Zeus. One of them wants to just leave it behind. The other...
Fake Cop: (in German) What are you doing! Some kid... Put it in the back!
That scene where Charlie walks into Cobb's office with a briefcase bomb:
Charles Weiss:[comes in] A nut who knows a lot about bombs. We found this in a playground. Professional. Very cool stuff! You know... [thuds the bomb roughly on Cobb's desk] Boom!
Inspector Walter Cobb: You think you should slam it around like that, Charlie?
Charles Weiss: It's unmixed. You can't hurt it. This stuff is cutting edge. It's a binary liquid.
Inspector Walter Cobb: A what?
Charles Weiss: Like epoxi. Two liquids. [puts a small dab of a clear liquid on Cobb's desk] Now, either one by itself... [hits it with his shoe] you got nothing. But, mix them... [swirls the edge of a paper clip in both liquids] Ricky? [Walsh moves aside and Charlie throws the paperclip at a chair. The mixture explodes and throws the chair all the way across the squad room]
Connie Kowalski: Charlie, you're gonna be wearin' that chair up your ass!!
Inspector Walter Cobb: Christ almighty, Charlie! [Charlie continues as if nothing has been said about his little show]
Charles Weiss: Like I said, very cool stuff. Now, with a package like this, you get a warning. Now, the bomb has to arm itself. You'll see the red liquid pump into the clear before it detonates.
John McClane: How long before?
Charles Weiss: Ten seconds, two minutes, it could be anything. But, once it's mixed, be somewhere else!
When Simon is calling the rear truck driver, Nils (who was one of many bad guys killed by John, unbeknownst to Simon), to inform him that they are at the dam.