h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Wouldn't plate tectonics, the difference of the surface's and core's rotation, and the mantle's convection slowly destroy the tunnel in which the vehicle would travel in?

Perhaps the most important problem is that we don't really know if the predicted oscillation would occur -- even under the most ideal conditions. So why not build a scaled down version of it first? This could be done with more convenient sized masses in a satellite experiment or by using a modified Cavendish balance in an Earth-based laboratory.

Other reasons for wanting to do such an experiment can be found at GravitationLab.com.