I think choosing Hillary would be a mistake. Not because of Bill. The new administration can choose to use him or not, regardless. The "two for the price of one" stuff is ridiculous: they are not exactly chained together. Equally, if Hillary were the best candidate for secretary of state, it would be absurd to deny her the offer because of Bill's post-presidential connections. Scrutiny in future is really all that is required there.
No, the problem is that she is not a well-qualified candidate. She is not by any stretch of the imagination a foreign-policy expert. I don't think I would call her a born diplomat. And her loyalties, to put it mildly, might be divided. Her first priority would be to advance her own presidential ambitions, not to help make the Obama presidency such a success that those hopes die. The "team of rivals" idea is wonderful so long as the rivals are fully invested in the success of the enterprise. In this case, it seems doubtful. Could Hillary defer to Obama, and carry out his instructions to the best of her ability? I doubt it. And it would not help that everyone would be watching for the first sign of friction or insubordination. The soap-opera dimension would be highly counter-productive.
I find Tom Friedman persuasive on this:
Foreign leaders can spot daylight between a president and a secretary of state from 1,000 miles away. They know when they're talking to the secretary of state alone and when they are talking through the secretary of state to the president. And when they think they are talking to the president, they sit up straight; and when they think they are talking only to the secretary of state, they slouch in their chairs. When they think they are talking to the president's "special envoy," they doze off in midconversation.
What is Obama thinking, I wonder? That the party would be delighted? Yes it would, but so what: the election is already won. Or is it something to do with keeping your friends close and your enemies closer? (LBJ put it less delicately of course, but the metaphor does not really work in this instance.)