Award Snub: Famously at the time. Bette Davis was thought of as a shoe-in as Best Actress for Of Human Bondage. But due to studio politics and campaigns against her, Claudette Colbert won for this. The snub was influential in causing the Academy to change its voting practises.
If the movie gets mentioned, most of the time it's going to be for Clark Gable's shocking Shirtless Scene - where he wasn't wearing an undershirt. Legend has it that it caused undershirts to drop in popularity.
There's also the famous, and often parodied, scene of Claudette Colbert flagging down a car by lifting up her skirt and exposing her bare leg.
Ear Worm: The bus singalong of "The Daring Young Man on the Flying Trapeze."
Peter opines to Ellie's father that she should perhaps be "slapped around a little", which doesn't affect her father's view of Peter at all (probably because it's entirely unclear whether he's serious, being hyperbolic in his frustration, or metaphorically saying that she needs more structure in her life).
Also, not a lot of of romantic comedies are likely to start from a pretty serious blackmailing these days...