Actor Allusion: Paul's "decorator" says to him, "Well, love has found Andy Hardy." Andy Hardy was the lead character of a series of films (including Love Finds Andy Hardy) portrayed by Mickey Rooney, who plays Mr. Yunioshi.
Audrey herself is a Fake American, though her foreign accent is explained as a result of speech lessons. In the movie the accent is so she can casually pass herself off as a Fake Brit, to make her more marketable as an aspiring actress.
Hey, It's That Voice!: Sally Tomato was played by Alan Reed — the voice of Fred Flintstone. It's worth noting that the film came out around the same time the series started, so you're seeing Reed at the time he began playing Fred. The physical similarities are particularly obvious.
Old Shame: Both Richard Shepherd and Blake Edwards had regretted of casting Mickey Rooney in Yellow Face. Mickey Rooney himself stated if he'd known that so many people would be offended, he would never took that role.
Referenced By: In an episode of Seinfeld, George joins a book club where he is supposed to read the novella but is too lazy to (despite its brevity). He rents the movie instead and is humiliated later on when he mentions that Holly hooks up with Paul at the end. He should have known about Adaptational Sexuality.