Among all the political qualities needed for a Vice-Presidential nominee (does he balance the ticket? carry a key state? have no skeletons?), one thing that gets mentioned insufficiently often is whether the candidate has the qualities that might make a good President. Veeps frequently end up either stepping in for the boss, or running on their own, so it matters to the country that they be of Presidential caliber.
History is littered with examples of candidates, and elected Veeps, who conspicuously lacked this quality:
Sipro Spiro Agnew and Dan Quayle Quail would surely be consensus choices. Many might argue Cheney belongs in this group, albeit for very different reasons.
Ex ante prediction about who will be a good President is a very imperfect science. On the day he was elected Vice-President there would have been something of a consensus that Truman lacked the necessary qualities (“to err is Truman” went the slogan), and yet Truman, flawed as he was, looks better and better in hindsight.
What I like best about John Edwards is that I think he has the making of a great President. He's a little green, especially about foreign policy, and a little too protectionist on trade, but a good eight years as veep could season him to perfection.
In picking Edwards, Kerry has put statesmanship over personal friendship (with Gephardt). He's also shown an ability to manage the media (whipping them into a frenzy for weeks), and to keep a secret. That looks Presidential right now.
Update: This New York Post 'Exclusive' is pretty funny.