Well, I saw the original interview and Jane was referring to one of the most famous monologues in the Vagina Monologues that's actually titled with the "c-word."
The whole point of that monologue is to confront that word or to try to re-claim it into something more positive (and to think about ways that might be possible or to question if that's desirable). The fact that people are so scandalized by Jane's simple use of the word in an interview about a play in which that word features prominently... sort of proves the point that the "c-word" monologue is trying to make.
I guess the main point, is that folks react so emotionally and so strongly to that word (in much the same way that they react to the n-word) because it's often associated with so much violence and hatred.
But, there is a fairly prominent strain in certain feminist discourses all about trying to appropriate that term as a "power word," etc. I suppose the Today Show audience isn't prepared for edginess or a confrontational stance so early in the morning.
Actually, when Jane said that word I think she was being very deliberate and was actually trying to act on some of the messages from that monologue in "real life."
I personally wasn't offended by it at all... in the context of how and why Jane said it.
And, on the topic of the word "dyke"... I think the issue of trying to "re-claim" the "c-word" is much the same. Although, I think "dyke" is much less offensive to begin with. Anyone who's familiar with the phenomenon of "Dyke March" pride parades will know that lots of lesbians have no problem at all with that word when using it themselves. I've actually participated in two Dyke Marches in Philly in the past. If a homophobic person uses the word "dyke" it's entirely a different matter, of course.