Well, I do agree about Bloody Mary and Shall I Tell You What I Think Of You.
Most of the songs from The Sound of Music could go without causing any plot problems. And much as I like it, I Enjoy Being A Girl from Flower Drum Song. Kansas City wouldn't hurt Oklahoma if it wasn't there. And that song that Mr Frake sings to the hog in State Fair (I know it is only in the Pat Boone film, but still ...).