Groucho: It says the, uh..."The party of the first part shall be known in this contract as the party of the first part."
After shredding nearly every part ("The party of this part shall be known...") of the contract out:
Chico: Hey, what's this part?
Groucho: It's all right, that's in every contract. That's what they call a sanity clause.
Chico: Ahaha, you can't fool me! There ain't no Sanity Claus!
And the reprise, in which the contract-ripping is one-upped by Harpo ripping the back of Gottleib's tuxedo coat.
THE Stateroom Sketch. On the steamship, Groucho is already dismayed to discover he's been given a broom closet sized room. He opens his trunk to discover Chico, Harpo, and his client Ricardo have stowed away. On top of it all, apparently every maid, electrician, carpenter, plumber, etc. is assigned to service their room at the same time. Groucho's deadpan reaction to a very large engineer's assistant showing up to help the chief engineer, after he'd already had a number of other people cram themselves in: "Ah yes, I had a premonition you'd be coming."
"...and two hard-boiled eggs." (HONK!) "Make that three hard-boiled eggs."
"Was that three guys with beards, or one guy with three beards?"
The three stowaways are thrown into the ship's brig. Fiorello (Chico) paces fretfully, Ricardo (Jones) tries to sleep: Tomasso (Harpo) cheerfully plays 'Cosi, Cosa' on a musical comb. Fiorello seizes the comb, opens the porthole, flings out the comb and slams the porthole shut again. Tomasso looks guilty until Fiorello turns his back, then pulls open the porthole and starts to crawl out after the comb!... but does a Double Take and ducks aside as fifty gallons of seawater gush into the brig, soaking the other two.
The stowaways disguise themselves as some famous aviators who are also aboard, and when they arrive in New York they're expected to give a speech to a massive crowd (and to radio listeners). Fiorello steps up.
Chico: The first time, we get halfway across when we run out of gasoline. We got to go back. Then I take twice as much gasoline. This time, we were just about to land, maybe feet...when, what do you think, we run out of gasoline again. Back we go and get more gas. This time, I take plenty gas. We get halfway over, when what do you think happened? We forgot the airplane. So we sit down and talk it over. Then I get the great idea... we no take gasoline. We no take the airplane. We take steamship. And that, friends, is how we fly across the ocean.
The scene where the chief of police tries to prove that the other three are hiding out with Groucho, with them progressively hiding the evidence (four beds) when he's not looking, which only makes him think he's going mad.
Henderson: Say! What's that bed doing here? Groucho: I don't see it doing anything. (later) Henderson: The last time I was in this room there were four beds in here! Groucho: Please! I don't want to hear about your private life, Henderson.
When Harpo, Chico, and the opera's orchestra conductor get into a baton-tapping contest with each other.
Groucho: Not that it's any of my business, but I think there's a brace of woodpeckers in here.
Within the opera scene itself, they trick the orchestra into playing "Take Me Out To The Ballgame"... and then start tossing a ball around. Including using a violin as a bat.
A performer uses a whip to tear off the skirt off a female performer, leaving a smaller skirt. Harpo uses another whip to tear the smaller skirt off of the performer, leaving her in tights and underwear. Groucho notes to someone in the audience, "Now we're getting somewheres!" Especially because Harpo then goes on a spree and just randomly rips the skirts off of the rest of the actresses.
Groucho's take on a gypsy woman in the opera: "Boogey boogey boogey!"
Harpo's hijinks while the tenor sings "Mal reggendo" and "Di quella pira." They put a battleship... and a streetcar... in Il Trovatore! One of the backdrops comes down in front of the tenor, leaving him to poke at it impotently, while still singing.