As Orpehum mentioned, there's been a lot of speculation about who or what Mr. Jones might refer to. Adam Duritz himself answered this question in part of the VH1 Storytellers show which was left out of Across a Wire for reasons of CD space:

"I have heard everything from it being about some ancient blues man who taught me to play music, which is completely ridiculous (but like somebody's movie fantasy). And I've also heard it's about my dick, which is even more ridiculous. Why do people go there, you know?

When we did the interview for "Rolling Stone" I walked with David Wilde into the Musée d'Orsay in Paris one day and the first thing that happened was these two kids ran up to us and said, "Hey! You're the guy from Counting Crows, right?" And I said, "yeah." And he said, "Is Mr. Jones about your dick?" I wanted to kill the guy because I knew where that was going to end up, which is the first paragraph of the article in "Rolling Stone." It's really a song about my friend Marty and I."

"Marty" here refers to Marty Jones, a bass player for Sordid Humor and The Himalayans - both bands with which Adam Duritz had played before joining the Counting Crows.


With thanks to Two Sheds for pointers and corrections.