Sisyphus you may be right, but things didn't go well with James either, a few seconds searching and there are way more hints than I thought.
http://wiki.answers.com/Q/Who_is_the..._Vain%27_about
Stuff that was new to me:
Update
There has been many updates. The letters A, E and R are in the name as clues given away by Simon herself and many other clues have lead to David Bowie. However, there is no 'R' in David Bowie of course. That is until you find out that David Bowie's real name is David Robert Jones.
Although the reference to Nova Scotia (Beatty's Mother from there), Saratoga racing and underworld spies would relate more to Warren Beatty.
-teaspoonofcement-
UPDATE
I've always thought the song was about Eric Clapton...and all of those letters are in his name, as well, so maybe I'm right. When you listen to the song, it says "you're with an underworld spy, or THE WIFE OF A CLOSE FRIEND...." that was my clue that hit me between the eyes. Eric Clapton wrote "Layla" for the wife of George Harrison, whom he took away from him. And I believe that Carly Simon dated Eric Clapton. So it's only a guess, but I believe that one of the reasons Carly won't give the answer out to the world is to protect Clapton, who's had a lot of sadness in his life, and who has turned his life around since that song was popular.
- Tiamoaz58 -