Gaslighting: When the team finally reaches america, they move beds from one room to the other to anger the detective.
Food Porn: The scene where Chico, Harpo and Ricardo finally get to eat will make any viewer seriously hungry for Italian food. Pasta with sauce, salamis, whole tomatoes, wedges of cheese, loaves of bread, and bottles of wine - all served on a single plate!
Driftwood: You're willing to pay him a thousand dollars a night just for singing? Why, you can get a phonograph record of 'Minnie the Moocher' for 75 cents." (Pause) For a buck and a quarter, you can get Minnie.
Driftwood: You see that spaghetti? Now, behind that spaghetti is none other than Herman Gottlieb, director of the New York Opera Company. Do you follow me?
Mrs. Claypool: Yes.
Driftwood: Well stop following me or I'll have you arrested!
Logical Fallacies: Half of the hilarity comes from Groucho's elaborate wordplay and mind games.
Driftwood: That woman? Do you know why I sat with her? Because she reminded me of you.
Mrs. Claypool: Really?
Driftwood: Of course, that's why I'm sitting here with you. Because you remind me of you. Your eyes, your throat, your lips! Everything about you reminds me of you. Except you. How do you account for that? (beat) If she figures that one out, she's good.
Only Sane Man: Subverted. They simply didn't have the budget for one. Everyone - even the straight-laced lovers and the evil Jerkass - gets sucked into the Marx Brothers' madness.
Overly-Long Gag: "And two hard-boiled eggs!" ". . . and two hard-boiled eggs."
"Make that three hard-boiled eggs."
Reality Subtext: A few jokes and references to the ongoing Depression. Probably the most serious one is when, towards the end of the film, Groucho goes up in the elevator to his office—met with friendly or sycophantic reactions by the opera staff and the elevator attendant—only to find he's been fired, and then they all immediately turn on him.
They're not above using it as material, either.
Mrs. Claypool: Six months ago you said you'd introduce me into society, and in all that time you've done nothing except draw a very handsome salary.
Driftwood: You call that nothing? How many men do you think are drawing a handsome salary these days?
Tough Room: Driftwood gives an opening speech at the opera that in real life would have brought the house down, but the only response he gets is stony silence.
You Get What You Pay For: Drifwood overhears that Lasparri is going to be paid one thousand dollars per night and decides to skim the deal somehow. He is clueless and assumes Fiorelos is Lasparri's manager, so he is willing to pay 10 dollars per night. He learns later that he was hiring Ricardo Baroni instead. It turns out Ricardo Baroni is an excellent singer, just unknown by the public.