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?
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.
"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 accidently mistaking Indy's whip for a snake and waves the torch towards it as Indy reels in pain
The monkey doing a Sieg Heil - and one of the Nazi goons reflexively returning the salute.
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.