Dr. Selden and the Starkeeper-
Is it implied that they are actually one and the same person? In the 1967 TV version of "Carousel", starring Robert Goulet, they were. That's what I remember most about it. In that version, Billy goes down to Earth with the Starkeeper himself, not with the Heavenly Friend, and the Starkeeper tells him later that he can't accompany Billy to the graduation because he has business to attend to - something that makes Billy notably uncomfortable. When Billy goes to the graduation - surprise! The Starkeeper is there, posing as Dr. Selden.
In the stage version (I have six of the R&H librettos in an old Modern Library hardback book), the stage instructions say that as Billy and the Heavenly friend pass by Dr. Selden when leaving, he "watches and smiles wisely". IMHO, that implies that our old doctor was really the Starkeeper, and that he went down to Earth to help Billy out of a jam after he slapped his daughter.