Given the length that a space elevator needs to be to be in geostationary orbit, that's one very very LONG meteroite wrapping itself around the equator as it comes crashing down.

I don't think we need worry that much. It's long but very, very thin. It's also going to be very fragile under certain types of distortion, as all the strength will be in resisting tension. Also, probably not much of it would enter the atmosphere. It would most likely fragment, and most pieces would be thrown into various shapes of elliptical orbit, as dangerous space debris. No part of the elevator design would include high-velocity re-entry, so any parts that hit the atmosphere would disintegrate pretty quickly.

It would be a very expensive disaster, because a space elevator would be very expensive. But dangerous? Not very.