In the opening, Harry arrives at a party in Switzerland, completes his mission and is walking out when he is accosted by a guard, demanding to see his invitation. Harry pulls out a cigarette case, and memorably says "Sure. Here's my invitation" and presses a button on the side, detonating hidden explosives he had planted earlier.
Also, at one point Harry asks a servant (in Arabic) where the bathroom is. Subtitles translate this as "Where's the bathroom? I need to take a major leak." Below that, a secondary subtitle that reads "(Perfect Arabic)"
Gibb is one of the funniest sidekick characters ever in an action film.
Gibb: Same thing happened to me with wife number two, remember? I have no idea nothing's going on, right? I come home one day and the house is empty, and I mean completely empty. She even took the ice cube trays out of the freezer. What kind of a sick bitch takes the ice cube trays out of the freezer?
Even funnier is this story comes at the end of Gibb trying to make Harry feel better about his wife cheating on him.
Will you stop cheering me up!
The entire Harrier sequence in Miami is comedic gold.
A mook hears a loud jet noise, and he and his counterparts get ready, while he scans the surrounding area with binoculars. Suddenly a large grey shape rises up outside the window, and he focuses his binoculars to see a very pissed off Harry Tasker, piloting a Marine Corps Harrier jet. Said mook no doubt shits his pants, and everybody opens fire, only to immediately get diced by the Harrier's GAU-12 cannon.
Aziz is chasing after Dana, and has her cornered on a rooftop crane. Suddenly she slips and falls, hanging on for dear life. As he closes in on her, the Harrier swoops in underneath. Aziz's dumbfounded reaction is priceless.
Later, Aziz leaps onto the Harrier and wrestles with Harry for control of the jet. As the jet spins around in mid-air, it passes by a janitor cleaning a room in another part of the building, completely oblivious to what's going on. The jet ends up slamming tail first into said room, launching Aziz backwards, landing crotchfirst on the jet's tailfin.
Finally, Aziz gets hooked on the wingtip missile of the Harrier, and the remaining mooks are in a helicopter on the other side of the building, visible through the damaged floor that was shot up earlier. What does Harry do? Engage the master arm, lock on to the helicopter, and launch the missile, and Aziz, with it, but not before delivering an epic line:
Where do we start with the shootout and first confrontation between Aziz and Harry?
Aziz fires at Gib, whose only cover is a light post. He turns to hide behind it, and the bullets can clearly be seen striking both the post and the area around it, but somehow managed to miss Gib entirely despite the fact that he clearly sticks out from both the front and back.
Gib's reaction: He feels up and down his body to make sure he hasn't been hit anywhere, ending with his crotch, before muttering "Oh thank God..."
The poor old man caught in the middle of the bathroom shootout.
Their vehicles for the subsequent chase: Aziz's motorcycle vs. Harry's commandeered police horse.
Harry:(gives directions to Gib to get backup to catch Aziz) All right, and make it happen quick, because my horse is getting tired. Gib:(beat) Your horse?
Harry:(after the horse refuses to jump from one building to the next and Aziz escapes) Now what the hell were you thinking? I mean, I had the guy, and you let him get away. (horse looks away; Harry pulls it back) Look at me when I'm talking to you. What kind of a cop are you, anyway?
By the way, that last scene merits a funny moment all its own. Aziz does a crazy stunt that involves leaping from skyscraper to skyscraper. Harry tries to follow, but that horse just isn't having it at all, and almost dumps him over the edge! You can just hear the horse thinking "are you CRAZY?!"
Harry's conversation with the torturer.
Samir: Is there anything you'd like to tell me before we start?
Harry: They're going to shoot us in the head, or they're going to torture us to death. Or they're going to leave us here until the bomb blows up.
Helen's first experience with a MAC-10. The recoil makes her lose control and drop the gun down the stairs...and it continues to fire, miraculously taking out every Mook in the room.
Topped by the look of impressed astonishment and stunned disbelief on Harry's face after he surveys Helen's handiwork.
As Helen is readying to shoot, Harry is busy struggling with another mook; when Helen's dropped gun starts to spray fire everywhere, Harry and the mook stop their fight and run for cover. On top of that, several mooks come around the corner, see the falling gun, and immediately try to run back (and get shot doing so).
James Cameron: "Oh, yeah, she's got her head in the guy's lap all right. Yahoo."
(mook nervously lowers camera and Aziz stops, throwing his hands up in a "What gives?" motion)
Mook: Battery, Aziz!
(There is dead silence as Aziz threateningly approaches him. And...)
Aziz: Get another one, you moron!
Mook: I think I have one—
Aziz: Shh! (raises silencing hand and shoos him away in annoyance)
Mook: ...in the truck. *runs*
When Harry and Gib are listening to Simon bullshitting over the wiretap:
Simon: It's the training. It shapes you into a lethal instrument. You react without thinking. Gib: I'm starting to like this guy. (notices Harry's Death Glare) Oh, we still gotta kill 'im. That's a given.
Their reaction to Simon taking credit for what Harry did: they can't believe the gall of it and even Harry thinks it's Actually Pretty Funny: a scammer lying to his wife about what her husband did.
The final line in the movie, after Gib is annoyed that Harry and Helen ignored him over the earpiece while on mission:
Gib: Y'know what? I'm sick of being in the van. You're going in the van next time. I've been in the van for fifteen years, Harry.
Gib finally having enough of Simon annoying him and Harry, and starts casually shooting at his feet.
Gib: (bored tone) Get lost, dipshit.
What makes this funnier is that Gib has been shown to be a sort of bumbling sidekick next to the awesome that is Schwarzenegger, but then he shoots at Simon and deliberately misses with such indifference you can tell he's really competent with a gun.
Aziz fist pumping in celebration after apparently blowing up Harry with a rocket launcher.
During the striptease scene, Harry has the taped dialogue asked Helen to dance. After she starts an out-of-place dance, the next message is "No no no, dance sexy." Harry correctly predicted she would dance like a goofball and pre-recorded dialogue to compensate for it.
Towards the end, Harry tries to be romantic, but Helen has no idea it's him and decks him with the phone. After kicking him a couple times, she retains the presence of mind to complete her assigned mission, going back to plant the bug on the phone.
When Gib tries to hide a transcript detailing Helen meeting up with Simon, Harry yells "GIMME DAH GAHDDAMN PAGE!" and smashes a window with his fist. It's hilarious in its own right, but it's even funnier if you know the filming context like the striptease accident above: Arnold was supposed to hit a window rigged with safety glass, but broke a real window instead. Tom Arnold played it with the speechless reaction that the scene called for, but one would imagine part of it was also seeing his co-star breaking a car window for real with an Offhand Backhand.
While Harry grills his wife from behind the one-way glass, Gib keeps interjecting.
Harry: Tell me about your husband, Mrs. Tasker. Helen: Harry?? What can I say? I mean, he's a sales rep for a computer company. Gib: So sex with him isn't exactly waving your flag any more? Helen: That is none of your goddamn business! Now what kind of questions are these?! Harry: You're in a lot of trouble, Mrs. Tasker, so I suggest you cooperate. If we want to know the most intimate details about your life, you'd better tell us. Helen: My husband is a good man. Gib: But he's not exactly ringing your bell lately, right? (Harry covers the mic) Harry: Let me handle this part, I mean, do you mind?
When Aziz lays eyes on Harry in the harrier jet, the Big Bad pulls a "WTF?!?" expression for the ages.
Surpassed by Harry finishing him off in a wonderfully, ludicrously over-the-top manner. We'll let Seanbaby elaborate:
"Due to the nature of evil, bad guys aren't always aware they're the bad guys. But let's say the very last of your friends are in a helicopter, it's hovering in front of Arnold's final missile, and your body is dangling from that missile. As you rocket towards hilariously impossible circumstances it'll probably hit you that shit like that never happens to the good guy."
The chase over the bridge; one of the harrier pilots, before firing at the bridge to take out Aziz's convoy and prevent them reaching the mainland with the second nuke, asks if there is a danger that they might set off the warhead. Harry reassures the pilot that it won't go off...but then throws Gib a look as if to say, "How the hell do I know?!?"
During the bridge chase, one of the terrorist vans breaks out their surface-to-air missile and two of the gunmen use it without realizing what the back-blast will do to the front of the van... and to another terrorist who gets blasted through the windshield.
The second terrorist truck avoids getting blown up when the bridge gets taken out, but is left precariously dangling over the edge. The driver and his surviving bad guys start laughing at their good fortune... only to watch a pelican nonchalantly fly onto the dashboard, forcing the truck to slide off the bridgenote Relax, the pelican is able to fly away unharmed. and explode in the debris below. Basically: Death By Pelican.
Juno's face when Helen decks Harry after he confessed he is a spy. She really enjoyed this moment!
Speaking of Juno, her "Oh, shit." just moments before the limo drives off the bridge.
The video game:
Whenever you shoot a civilian, the action briefly freezes as a text box pops up and Gib warns you: "For goodness sake, Harry, watch out for the taxpayers. This is an election year after all!" Do it again, and Gib further warns you: "Harry, you hit ANOTHER civilian!" A third time: "Normally, a deranged psycho like you would be seen as an asset in a government agency. However, this is a highly public situation. The mission's a wash and you've blown your cover. Now you'll have to restart the mission."