In 1912, as a young Indy and fellow Boy Scout Herman stumble upon a bunch of bandits who discover the gold cross:
Herman: (discovers a snake has been crawling on his leg for some time, starts promptly freaking out) Young Indy: Hey, it's just a snake.
He even picks it up and tosses it away as he said that!
In a way, the entire opening sequence of Young Indy getting into trouble is funny in how it sets up all the traits and skill sets we'll see in the older version. Especially the bit where Indy develops his phobia of snakes...
Also, "Fly, yes! Land, no!" What makes this funny is that Harrison Ford is a rather successful pilot in real life. What makes it even funnier is decades later, he ended up crash-landing a WWII vintage plane (he was injured, but not seriously so).
Jones, Sr.: Junior, there's something I have to tell you... Indy: Don't get sentimental on me now, Dad. Save it for when we get out of here. Jones, Sr.: The floor's on fire. See? Indy: What? Jones, Sr.: ...And the chair!
"Dad!" "What?" "DAD!" "WHAT??" "DAD!!" "WHAAAT?!?" "Head for the fireplace!"
When they wind up on the opposite side of the secret door in the fireplace, they're in a communications room of some sort, at which point a woman looks up and notices them. They both give her awkward grins. She grins back... and yells, "ALARM!"
Trying to escape the castle, Indiana is frantically looking for an exit and Jones Sr. sits on a chair that opens a secret staircase. Indiana proceeds to tumble backwards down the entire stairwell.
In the Venice chase, the pursuit ends up leading towards two giant boats... which are getting closer together, but a distracted Elsa doesn't realise at first. There then follows a classic misunderstanding...
Indy: Are you crazy, don't go between them! Elsa: Go between them? Are you crazy?!
Only after they (barely) squeak through does Indy explain that he was saying not to go between the two ships. Also a blink-and-you'll-miss-it Accent Relapse on Elsa's part; she's so freaked out by what she just did she says "betveen".
When they're on the zeppelin, talking about their...mutual love interest above:
Henry: You know, sharing your adventures is an interesting experience. Indy: That's not all we shared. It's disgraceful. You're old enough to be her fa—her grandfather! Henry:(Shrugging) I'm just as human as the next man. Indy: I was the next man!
The little smirk he makes after he says it is hilarious.
The way Elsa gives Indy the "Austrian goodbye", kissing him passionately and sucking at his lower lip while Indy is still enraged at her betrayal and doesn't respond or look at her directly.
And right after that:
Colonel Vogel: And this is how we say goodbye in Germany, Dr. Jones. (Punches Indy in the face, causing him to bump heads with Henry Sr.) Indy: I liked the Austrian way better. Henry Sr.: So did I.
When Elsa says to Indy that she'll never forget the time they spent together, Henry thinks she's talking to him and complements her. Indy shoots his dad a disgusted look over his shoulder that defies description.
The scene where Indy sneaks into the Nazi rally in disguise and runs into Hitler... who thinks Indy's just a starstruck fan, and autographs the notebook containing instructions on how to find the MacGuffin, and then gives it back to him. How humiliating must it be to get an autograph from the devil incarnate!
One can't help but imagine the look on any future archeology scholar's face who might be studying the book for notes only to come across a page signed by Adolf Hitler of all people.
"How does one get off this thing?" "(Brody gets knocked off the tank accidentally)" Made even funnier when Henry notices that Brody's no longer on the tank - you can see him lying there in the background, dazed and probably wondering what the hell just happened.
And then a moment later:
Jones Sr.: Where's Marcus?
Sean Connery squawking like a seagull to scare a gigantic flock of seagulls into the air.
They then cause the approaching Nazi plane to crash.
And then he just strolls back looking ever so pleased with himself.
The scene where they're trying to infiltrate the Nazi castle that Henry Sr. is being held in. Indy has a hilariously atrocious Scottish accent, Elsa's wearing the intensely out-of-place fedora, and to sum it up:
Butler: This is a castle...and we have many tapestries...but if you are a Scottish lord, then I AM MICKEY MOUSE! "Lord Clarence MacDonald": How dare he? *knocks out butler*
And when Indy comes crashing through the window of the room his dad is being held in, his dad cracks him over the head with (what he thinks is) an incredibly valuable Chinese vase. His dad is heartbroken at the loss, until he realizes it's a fake. Indy is more concerned about his possibly fractured skull.
Even funnier is the fact that in the novelization, Indy does this earlier at Barnett College to reveal that a fellow professor was cheated out of $300 for an alleged Pre-Columbian fertility idol.
One of the German pilots actually trying to fly into the tunnel to chase after Indy and Henry, tearing off the plane's wings and setting it on fire, and ending up passing their car. The look on the pilot's face just says, "I did not think this through."
This film remarkably has a Tear Jerker, Crowning Moment of Awesome, Crowning Moment of HeartwarmingANDCrowning Moment of Funny all at the same time without a word of dialogue. When Henry Jones Sr., Marcus and Sallah watch the tank which they think Indy's inside go over a cliff, they all stand heartbroken on the edge of it. Indy gets up and dazedly walks to the cliff edge, staring confusedly along with everyone else as if to say "What are you guys looking at?".
Indy also gives a little nod as if to say "Yeah, take that, jerk."
As an added bonus, is his hat rolls right back in front of him after that entire scene, as if going "Is it safe to come back now?"
Even funnier is Marcus' reaction to Indy's survival he, much like us the audience, were wondering how the hell he survived such a close call.
When Sallah meets Marcus, they are immediately intercepted by Nazis posing as museum attendants. Sallah sees right through the disguise, and desperately yet quietly tries to warn Marcus, who just can't take the hint.
The classic Gilligan Cut, from Indy giving an awesome, totally straight-faced lecture to the Nazis that they'll never be able to find Marcus as he'll blend in perfectly with the locals:
Elsa: It's perfectly obvious where the pages are. He's given them to Marcus Brody. Professor Henry Jones: Marcus? You didn't drag poor Marcus along did you? He's not up to the challenge. Walter Donovan: He sticks out like a sore thumb. We'll find him. Indiana Jones: The hell you will. (everyone looks at him with surprise) He's got a two day head start on you, which is more than he needs. Brody's got friends in every town and village from here to the Sudan, he speaks a dozen languages, knows every local custom, he'll blend in, disappear, you'll never see him again. With any luck, he's got the grail already.
Marcus: Does anybody here speak English? Or even Ancient Greek? Water? No, thank you sir. No...no, fish make love in it. Chicken? No thank you, I'm a vegetarian! Does anyone understand a word I'm saying?!
And when Sallah tells Marcus to hide in a nearby shop, which is, in fact, a Nazi truck that drives off. Sallah can only stare and lean over in disappointment.
Still later, Indy expresses a need to rescue Marcus, whereupon Professor Jones says "I thought you said he would blend in, disappear." Indy rolls his eyes and says "Are you kidding? I made that up. You know Marcus, he got lost in his own museum once."
As above, almost any time that Denholm Elliott (Marcus) is onscreen, he hams it up for all he's worth, including at the end when everyone is set to ride off into the sunset for a Happy Ending.
Marcus: Indy! Henry! Follow me! I know the way! Hyaaaaahhh! (Spurs his horse, which takes off, bouncing him violently in the saddle) Henry (sighs): Got lostin his own museum, eh?
That's actually a moment of awesome for Denholm Elliott, who in reality was an experienced horse rider, with enough skill to do his own riding in that scene and make it look like Marcus was going to wipe out.
Henry: What are you doing? Get down! Indy: Dad, we're well out of range. BOOM! (Sallah's car was hit) Sallah: That car belonged to my brother-in-law— Indy: COME ON!
It becomes a Brick Joke when Indy angrily tells Sallah that he doesn't need camels. Sallah explains they're not for transportation - they're to pay his brother-in-law back for the car.
This exchange between Indy and Henry Sr. after it comes out that Indy brought the MacGuffin with him:
Henry Sr.: I should've mailed it to The Marx Brothers. Indy: Will you take it easy? Henry Sr.: Take it easy?! Why do you think I sent it home in the first place? So it wouldn't fall into their hands! Indy: I came here to save you! Henry Sr.: Oh yeah?! And who's gonna come to save you, Junior?! Indy: I told you...*seizes a machine gun from a distracted guard, then mows away everyone with it, leaving his dad totally shocked*...don't call me "Junior"!
"Look what you did! I can't believe what you did!"
The best part is that it's James freakin' Bond getting upset over some bad guys getting killed.
It's his tone that sells it, not the horrified reaction one would expect from someone who just saw their child murder a bunch of guys, but a scolding tone as if he dropped a plate.
"What about the boat? We're not going on the boat?"
When the Nazis offer the Sultan a chest of jewels and gold, he is not impressed - he is impressed by the Rolls Royce, however. Donovan quickly adjusts his plan, smiles, and tells the Sultan, "The keys are in the ignition."
And when he says he'll offer them vehicles, provisions, and "tanks" with his accent, Donovan replies with "you're welcome".
"You call this archaeology?"
Indy laughing after killing the last Nazi motorcyclist chasing them, then doing a double-take at his father who just frowns disapprovingly and then casually winds his watch. Indy then glowers like he's thinking "Nothing's ever good enough for him!"
Before the front wheel explosion, Henry was clearly impressed that Indy was using a flag pole as a jousting lance.
Indy's bemused look when he somehow manages to kill three Nazis with a single shot from a Walther P38 pistol, the 9x19mm bullet passing through them all like they were cardboard cutouts.
When Indy is teaching a class and all the girls are gazing at him!
I swear, there are more girls this class than in the first movie. Makes you wonder how many female archaeologists were running around after World War II...
Unless they only chose his class because of the teacher.
When we find out where Indiana comes from. "The dog? You are named after the dog?"
"I have a lot of fond memories of that dog."
After dispatching one of the fighter planes in the tunnel.
Henry Sr: Well, you can't get much closer than that! (Cue the remaining plane dropping a bomb near them, causing them to crash their car into the resulting crater)
Indy and Vogel are fighting atop the tank and one of the Nazis in it is watching from the periscope. When Indy rolls over and accidentally smashes his face on the periscope, he grins amusingly, turns and says to his fellow officers in German, "Die Amerikaner, die kämpfen wie Weiber!" translation Those Americans, they fight like hussies!. Indy in his struggle, unintentionally kicks the scope causing it to turn inside and hit the soldier from behind.
"This is intolerable!"
Sallah's introduction to Jones, Sr. while the latter is dangling from a tank.
"Father of Indy, give me your hand!"
He even tips his hat while saying it!
The Knight has a bit of a sense of humor when meeting Indy.
Knight: The last of the three brothers, who sworn an oath to find the grail and to guard it. Indy: That was 700 years ago. Knight: Long time to wait.
Dr. Jones tells his students that "X marks the spot" never ever happens. Then it becomes a Running Gag that everything is marked with an X. When he sees an "X" scratched on a stone wall leading to the tomb, he rolls his eyes.
This little exchange from Indy and Henry Jones, Sr.'s argument over going for Brody or recovering the diary, which is also a moment of awesome.
Henry Sr: I wrote them down in my diary, so that I wouldn't HAVE to remember them. Indy: Half the German Army's on our tail, and you want me to go to Berlin? Into the lion's den? Henry Sr: Yes! The only thing that matters, is the Grail. Indy: What about Marcus? Henry: Marcus would AGREE with me. Indy:(incredulous)Two selfless martyrs, Jesus Christ (Henry Sr. slaps Indy lightly in the face, and responds with the Death Glare.) Henry Sr: That's for blasphemy.