Some Last words, and I will silence myself forever on this subject.
First regarding Mary Martin. Rodgers and Hammerstein pretty much wrote the thing with Martin in mind for the Nellie character. (In fact, as she states in her autobiography, she had some input over the development of the show.) Mary Martin had a knack for playing young, innocent, and idealistic and with the illusions that one can create on stage (no close ups, more lights and makeup) it was possible to see her as being that way. It was also, especially after Peter Pan, the type of role that audiences expected to see her in. I mean, hey, she won a TONY Award for playing Peter.
On the other piece of this, the age thing, take a look at the book of the play (which the movie version is based on). There are references in the thing to "older men and younger woman" relationships, such as the classic line, "Mother thinks that older men are better for girls". OR the crack about Captain Bracket's age and virility, and his angry comeback on how a younger woman could possibly find him attractive.
There is also the lyrics to Emile's Soliloquy "This is what I've longed for someone YOUNG and smiling climbing up my hill...YOUNGER men than I am, officers and doctors, probably pursue her. She could have her pick." Why would he refer to her and his competition as younger if they weren't, at least in comparison to him?
While it's true that naivete and narrow mindedness are not just the province of the young, I would think that the words of the playwright and the lyricist would speak for themselves. And the words of Michener himself who says that Emile is a "man in his forties" and Ensign Forbush is a "young girl".