First, the design depends on... the design :). Maybe with the new design it's going to improve :)
Other than that, I'm not sure it's an affordance problem as such. It looks and behaves exactly the same as all the other controls in that column - the vote up/down, favorites, FB and twitter. I agree that its affordance isn't perfect, but it's exactly the same as for all these other controls.
I thinks it's more of a motivation problem. Before I accepted my first answer, I saw a little red message on my profile, asking me to consider accepting an answer. But once I did it for the first time, it apparently signals to SE that I'm aware that answers should be accepted, so I never saw that message again. I think that if it appeared for all unanswered questions - both in the profile tab and on the question itself when viewed by the OP, it would increase acceptance rates.
In other words, I think users aren't sufficiently aware of the fact that it's important to accept answers, and the problem is not with figuring out how to do it.
But to answer the actual question itself - I think that it would help to turn the button into a box that appears on each answer and has both the icon and a call-to-action text, e.g. "Accept this as a good answer" or something. It would also need to be somewhere above or under the answer, and not to its left in the votes column.