NewScientist is reporting that while the strength of the tether has long been considered the main problem in building a space elevator, a new study suggests that a dangerous wobbling problem
may also be a serious obstacle. "Previous studies have noted that gravitational tugs from the Moon and Sun, as well as pressure from gusts of solar wind, would shake the tether. That could potentially make it veer into space traffic, including satellites and bits of space debris. A collision could cut the tether and wreck the space elevator."