I think he's generally perceived to have payed for Chappaquiddick. But for it, he'd have almost certainly been president, after all. I agree that these things deserve air-time though; in Kennedy's case it's an extremely important part of his story. Everybody likes a good tale of redemption.
On the one hand, I suspect the right fears that any sort of post-mortem badmouthing of Kennedy could also give the liberals a boost in the health-care debate. Alternately, well, he was an insider, an elder statesman, and a master of the deal, so it's probably equally true that large portions of the right are disinclined to pile onto him, no matter how much they disagree with his politics.
EDIT: liberal standard-bearers for the future? Russ Feingold, Henry Waxman, Barney Frank.
It's sad, but I feel like Feingold has already been relegated to a fringe-y sort of irrelevance in the media narrative. Not that this is irreversible (and I see it as something of a badge of honour, frankly), but I suspect his influence in the party and government is therefore pretty sharply capped at present. I'd love to see that change, and he's certainly still young enough to turn it around, and should there be (hope hope!) any sort of progressive/centrist split in the party, I'd expect to see him at the forefront.
Waxman's definitely important, but the man is also 70 years old; I suspect he's pushing the height of his influence with Energy and Commerce (not that this is insignificant!).
Frank's sort of the same situation; he's the same age, though he seems a little bit more vigorous to me. He could have Kennedy's seat if he wanted it, of course, but I'm not sure a couple of terms as a junior senator beats out head of Financial Services. Still, he's a bit more outspoken, a bit more charismatic than Waxman, I could see him easing into the role of the spiritual leader of the progressive left.