Even funnier, if you pause just as the nuke is seen above the testing site, it seems that the Government has the same idea to use "I Like Ike" on the side of the weapon. So, like "I Like Ike" were nearly Indy's last words, "I Like Ike" was the last words that the Russian Mooks heard/saw trying to escape from the testing site.
When Indy finds Oxley insane.
Oxley, its Indy. We went to school together at the University of Chicago and you were never this interesting.
"Damn! I thought that was closer!"
Indy and Mutt butting into the school library with a motorcycle and the ensuing scene with the student.
Indy: You want to be a good archaeologist, (Mutt drives them out of the building on his motorcycle) you've got to get out of the library!
Student: (looks after them mildly confused)
Similar to Indy and his father riding a motorcycle.
Like his father, Indy was not amused at Mutt's driving. Mostly because he just decapitated the statue of his old friend Marcus Brody.
When Indy, Marion, Oxley and Mutt are running from the Soviets' campsite (provoked by Mutt's own Indy Ploy), Indy says "This is intolerable!" Apparently now that his old man is dead, Indy is picking up his speech mannerisms (a thing that people with recently dead (grand)parents will attest is often Truth in Television).
And Indy actually takes his hat off just before the third drop.
The bit with the drysand pit:
Mutt: Grab the snake! Indy: Stop calling it that! Call it something else! Mutt: It's a snake, what do you want me to call it? Indy: A rope! Mutt:What?! Indy: Say, "Grab the rope!" Mutt and Marion: GRAB THE ROPE!
The Jones gang almost being pushed off the cliff, whilst Mac yells "This is VERY dangerous!" in a hysterical voice and Oxley laughs maniacally.
The nuclear testing ground. The overly bright colors and happy figurines just scream The '50s so well that it borders on parody.
When they are attacked at Orellana's Tomb, one of the attackers was about to shoot a poison dart at an unsuspecting Mutt, only for Indy to blow it right back into the attacker's throat. This mirrors the same trick Bugs Bunny used in the Looney Tunes shorts "Bushy Hare" and "Pre-Hysterical Hare".
The argument between Indy, Mutt, and Marion after Mutt finds out that Indy is his dad. He takes it better than that other kid, though he also spends some time in denial. Then the Soviet guarding them is so annoyed by the continued arguing that he gags Marion - who is still able to shout despite her mouth being tied shut. (She must have had some practice after Raiders.) And then all three of them overpower the guard before the big Jungle Chase.
Indy and Mutt starting a big fight between jocks and greasers at a malt shop to escape Soviet agents. The funny part being, you really don't know why Indy told him to punch Joe College... until he backs up into his friends, all wearing the same jackets... and a bunch of guys dressed like Mutt back him up... THEN you go "ooooooooohhhhh", and the fight music starts.
The best part? While Indy and Mutt are running away from the agents they make a turn and drive by the shop again, to find that the jocks and greasers (and some of the girlfriends) stillduking it out!
When our heroes begin their escape from the carvan, Marion slides into the driver's seat of the truck while Indy ducks into the back for a weapon as if it's completely old hat for them. Equal parts Funny, Heartwarming, and Awesome is the look Mutt gives his Mom. He's probably never seen his mother in action before, and now he's both confused and a little awestruck. "Wow. My parents are a Battle Couple."
Here's something ironic. When Indy cautions Mutt about how it's not wise to bring a knife to a gunfight, well, Mutt should trust him on that one.
The killer ants try to take Indy's hat.
The scene prior and after Spalko uses the skull on Indy. When Indy says he's gonna break your nose, it doesn't matter if an alien skull messes with his head he'll do it. Just ask Mac.
Indy: Eventually, they're gonna let me out of this chair, comrade, and when they do, I'm going to break your nose.
-Minutes later they let him out of the chair and Indy punches Mac.-
A meta-example. When Harrison Ford appeared on The Tonight Show to promote the movie, Jay Leno played a "clip" from the movie—an old man hobbling along with a walker with the theme tune playing, obviously poking fun at Ford's advanced age. As the audience roared with laughter, Ford, not to be outdone, cracked, "Actually, that's my stunt double."