The Coulterites crow that 'Ann beat Jeremy'.
I loathe Coulter like a slug in my salad but FWIW I think that if the interview is considered as an end in itself, a battle with no back-story or future implication, then she might be considered to have 'won'. Paxman didn't come across as a man playing for a win, but as a befuddled naif.
'Aren't you worried that you might damage the causes you believe in?' he naively asks. It's a rational question from a rational actor, used to dealing with political animals, whose actions are directed at achieving some end.
'I sell more books!' says Coulter. Because she isn't actually aiming at anything except the proliferation of Ann Coulter. She has no long term strategy, she has no true beliefs, and hence no worries about damaging them.
She says 'There is no evidence for evolution' and Paxman says 'Do you really believe that?'. It is the question of a man who has faith in words as a means to convey thoughts. Ann has no such restraint - words are tokens; she doesn't actually have any abstract beliefs. She 'wins' by saying 'I believe everything I have written, you can take that for granted'. And Paxman has no response.
IMHO the way to beat her is to take her at face value. Not to say 'How can you say such things?', but to say 'You seem quite ignorant'.
ETA - Yipes, I don't know how technorati works but now it's got a link to this blog entry. That was quick.