I've always liked the idea of space elevators, but I've also been bothered by a problem that I've never seen addressed, "micrometeoroid erosion". Sure, you can build one. But how long is it going to last, with nothing to protect the main cable/strands/shaft/whatever-you-want-to-call-it from a near-endless --though admittedly low-rate-- series of impacts by speedy dust particles?
I imagine they'd do something similar to how some of the new suspension bridge cables are designed. The main cables are actually cable bundles, and they're made so that individual strands can be replaced if necessary.