Yea i would imagine it spinning out of control but i can´t see how it will impact the earth if the forces applied to it is identical all the way around.
And assuming gravity is the same all around the earth and the earth is a perfect sphere for the arguments sake.
It does not have to spin, just any minute difference in distance between the bridge and the surface would be amplified, so one point of the bridge would come down to ground while the other side (I am assuming the thing holds it's shape at least until contact, which is probably false, but ok), pops up.
You can mathematically assume perfection, but even a perfectly spherical airless earth would bulge from tidal forces of the moon and sun.
Much earlier than touch down it should start to bend and crumble. Precisely 'how' would need tricky finite element simulations, not something that you can simply answer with rule of thumb estimations.