Dick Powell and Olivia de Havilland
Dick Powell sings "You Must Have Been a Beautiful Baby" and later dresses in blackface and does a Jolson impersonation.
Penny Singleton (from the Blondie movies) as Maggie's personal maid
Melville Cooper (Sheriff of Nottingham from The Adventures of Robin Hood) as Mr. Richards' valet
Tom Fadden* (the toll keeper from It's a Wonderful Life) as a gas station attendant
Looks like I was wrong about this one. It was Irving Bacon.
*IMDb doesn't even list this one!