There is an excellent technical review of the space elevator and related concepts (e.g. tether/slingshot) in Zubrin's (Ed) "Islands in the Sky". (An excellent compilation of articles:
http://en.wikipedia.org/wiki/Islands...lonizing_Space)
Apart from the materials issues mentioned above, the biggest problem is the required width of the tether at ground level -- it MUST taper as it rises (even using nanotube windings).