[KineticLensman]

The amount of reflected Earthlight would depend on your location on the Moon's nearside and the phase of the Earth.

The corollary of one side of the Moon always facing the Earth is that the Earth hangs in about the same place in the sky for any given point on the Moon's surface. Over a period of (earth) days the Earth's position would slightly but visibly oscillate due to libration [0]. This might slightly vary the incoming Earthlight (analogous to the Moon's illumination at the horizon vs. at the Zenith).

A much bigger effect, however, would be due to the phase of the Earth. As the Moon orbits it will sometimes be between the Earth and the Sun, sometimes further away. On the sun-side, the Earth would be more 'full' and thus there would be more light to reflect. This would significantly vary the incoming light.

[0] https://en.wikipedia.org/wiki/Libration

[philwelch]

A "full Earth" would coincide with the sun fully illuminating the far side of the Moon, and a "new Earth" would coincide with the sun fully illuminating the near side of the Moon, so wouldn't you only get maximum darkness anywhere on the Moon during a lunar eclipse?

However, counterintuitively, I think you'd be better off with a full Earth and no direct sunlight than a new Earth and full direct sunlight, making the near side a slightly better place for an optical telescope. The near side of the moon even has the opportunity to experience eclipses.