The film opens with Indy braving death traps, scary spiders, waves of angry natives trying to kill him, and he pretty much takes it all in stride. Get him on the plane with a snake as a fellow passenger, though...
Indy: There's a big snake in the plane, Jock! Jock: Oh, that's just my pet snake Reggie! Indy: I hate snakes, Jock! I HATE 'EM! Jock: Come on! Show a little backbone, will ya?
After Indy escapes the temple, he is surrounded by angry natives along with one of the treacherous guides from earlier, the natives knock the person down to reveal that his entire back is covered with darts.
What Marion says when she gets abducted by some of the thugs in Cairo.
Marion: You can't do this to me, I'm an American!
The scene of Indy facing down a swordsman in the Cairo market. The Mook spends several seconds twirling the blade menacingly, after which Indy makes a "I don't have time for this" face, pulls out his gun and shoots him.
Better: that look on Indy's face is actual pain from Harrison Ford's dysentery that forced the "just shoot the sucker" moment in the first place.
Even better than that, the natives swooping in on the guy's corpse and stealing his sword, cheering enthusiastically.
Also lucky that the real-life swordsman they hired for the scene turned out to be so good at pratfalls.
The music. It starts suspensfully when the sword man appears and starts doing his tricks, then it gets whimsical when Indy picks up the gun and shoots him.
"Asps. Very dangerous. (taps Indy on the shoulder) You go first."
Most anything Sallah says or does is pretty good for a laugh.
"I'm so pleased you're not dead!"
During the desert chase, two Germans on a motorcycle & sidecar ride up to the truck Indy's driving to try and take a shot at him. Indy flashes a quick "who are they kidding?" look, quickly yanks the steering wheel in their direction, and then looks back to see the bike and its two riders tumbling off the road and into a ditch.
Indy stealing the uniform of the Officer that questioned how badly the first uniform he stole fits him.
Blink and you'll miss it, but you can actually see Indy sizing up the officer, trying to see if his clothes are the right size before knocking him out.
The DVD special features have some utterly hilarious footage of Spielberg chastising one of the snakes from the Well of Souls scene after discovering that, being cold blooded, snakes actually like to be close to fire. "You like fire. In the script, you're supposed to hate fire. Why do you like fire?! You're ruining my movie!"
Marion waving the torch at Indy's whip mistaking it for a snake and causing Indy to jump in pain.
And it's based on a deleted scene from 1941 (done for that film by Christopher Lee!), which Spielberg swore he'd try to put in all of his movies until it stayed in.
Indiana's reaction to Belloq's mocking as he's trapped in the Well of Souls:
Belloq: "What a fitting end to your life's pursuits. You're about to become a permanent addition to this archeological find. Who knows? In a thousand years even you may be worth something."
Indiana: (smiling nervously, doing a forced laugh) "Ahahahahh!..." (under his mouth) "Sonofabitch..."
In the bar fight, Indy and a Mook are grappling over a gun and another mook is told "Shoot them. Shoot them both." They promptly, of one mind, both turn and shoot the other mook.
Along the same lines as that bar fight, Indy and the driver of the truck joining forces to avoid crashing (much) into a construction project and then sharing a moment before Indy punches him out of the truck.
While Toht is a frightening character. Seeing him jumping out of the bar after touching the hot medallion and whimpering in the snow is amusing to watch.
Marion and Belloq powering through a bottle of grappa and being reduced to helpless giggling.
"Love" and "You" on a sighing young girl's eyelids.
And Indy's flustered response.
Just look at that classroom! More than half of the students are young girls just gazing at their archaeology professor.
The monkey doing a Sieg Heil - and one of the Nazi goons reflexively returning the salute, before getting a look on his face of "What the hell did I just do?"
Funny in a kind of darkly way to some, The Reveal at the end of the film which implies that the government strong-armed Indy into handing the Ark into their hands so it could be studied properly... only to promptly stuff it in a huge warehouse to be (quite possibly) forgotten.