> Could you generate nontrivial power from the Moon's motion through the Earth's magnetic field?

Not sure, but my gut feeling says no: the Moon is a very long way from the Earth relative to the Earth's size, therefore the magnetic field is likely to be fairly uniform around the Moon and so that can't extract much work.

That said, one fun idea I've had is to just assume that the Dark Energy expansion of the universe is pushing the Moon away very slowly; 73 (km/s)/Mpc * distance to the moon ≈ 9.5e-10 m/s, which is pretty close to the actual current Moon-Earth recession speed.

Plugging that into the formula for far-field gravitational potential energy given the mass of Earth and the Moon, that's about 170 GW at the present time.

(But don't go trying to crowd-fund a Dark Energy field reactor on my say-so: At my [rather limited] level of understanding, it looks like physicists haven't yet reached any sort of consensus as to whether or not Dark Energy might work like that).

I'll shoot you the DEFCoin white paper.

My gut feeling says that it is not impossible but you would probably need many loops around the moon to generate a sufficient coil, making the whole thing cost prohibitive. You could probably dot some solar farms around the equator of the moon and loop them all up with a big cable for a fraction of the price.