Let's suppose we have a rope with more than 10% elasticity (relative delta of distance)
The earth is always visible from the near side of the moon (that's the other half from what people erroneously call the "dark" side).
If the moon was always visible from one of the poles (like the sun is for almost half a year) you'd only need to compensate approximately 360°/24h (the moons orbital rotation of 360°/month doesn't matter much) with something like a slowly rotating swivel.
But that's never the case, I suppose the moon is at best only visible for 18 days in a row IIRC.
So you'd end up constructing a large tower in Antarctica, such that from top the moon is always over the horizon.
No idea how tall this tower must be, but if it crosses the atmosphere (I'm pretty sure it must¹) this would also solve the problem of a giant whip lashing thru air.
All the construction problems aside, I wouldn't be surprised about electrostatic problems arising from connecting two giant bodies.
Can't see the benefit of such a construction, that's at best a theoretical question for math class.
PS: pollsters seem to be desperate. ;-)
¹) too lazy for calculations, but alone with an ecliptic angle of 23° something like 1-3 thousand km would be "reasonable".
Quick calculation say a tower on the pole needs roughly 1000km height (at least) to be able to see the moon all year from the tip. (6371/cos 30° = 7356 )
Well that's already 3 times higher than the ISS orbit...
In reply to Re^3: What would be the most significant thing to happen if a rope (or wire) tied the Earth and the Moon together?