Badass Decay: In a sense that Driftwood being fired from the Opera Company is the first time that Groucho isn't on top of things.
Crosses the Line Twice: Driftwood's rude, abusive, screwy, cheap and thieving schemes are hilariously despicable... or despicably hilarious! Choose one. Better still, take two and call me in the morning!
Harpo's solo performance of "Alone". A lovely song, and perhaps Harpo's best performance in any of the movies.
The Marx Brothers picked exactly the right opera to send up. The plot of Il Trovatore makes very little sense anyway (partly due to the librettist chopping out more than half of the story in between acts), but the music can stand up to anything.
Designated Villain: Lasspari is at least unpleasant enough that the audience wants to see him eat humble pie, but Gottleib is never portrayed as anything but a decent man looking out for his opera and his investors. Sure, he doesn't like Driftwood, thinking him a cheat, a hustler, and a fortune hunter... but Driftwood is all of those things, and he has no particular grudge against Tomasso and Fiorello until they break into his business and start ruining his show and repeatedly injuring his head. On the other side Gottleib was absolutely ok with helping Lasspari ruin Rosa's career because she rejected his advances and only gave Ricardo a chance when he was literally his only hope.
Iron Woobie: The titular character in "Bohemian Rhapsody", who is apparently "a poor boy who needs no sympathy" and nobody loves. He kills a man and feels bad for it, yet at the same time "nothing really matters to [him]" and he decides to face his fate.