The short answer: for optical astronomy (IR through gamma wavelengths), no, there isn't any huge advantage. But for radio astronomy there are distinct advantages to being on the lunar far side, they're just not related to any albedo differences.
Electrostatic forces loft tiny (micron-sized) dust particles above the moon's surface. When lit by sunlight they cause background light levels roughly comparable to those at good observing spots on Earth, so there's no advantage there. At night (which lasts about 14 Earth days) those dust particles are not lit, so there is the minor advantage of lower background light levels for optical observing.
That dust is the source of a distinct disadvantage: it can coat optics. And lunar dust isn't like Earth dust. It is hard, angular, and extremely abrasive, (same reference as above) so you can't just brush it off a mirror's surface—it would scratch the heck out of that surface!
For radio astronomers, especially those wanting to do radio astronomy at very low frequencies (tens of MHz and below), the far side of the moon would be the perfect place for observations (see this ESA PDF). Earth itself is a cacophony of radio signals at every frequency. For a Star Trek 4 analogy, for long-wavelength radio astronomers Earth is the guy on the bus with the blaring boom-box. The far side of the moon would shield against the great majority of that noise. And at night, when the sun (also a significant source of radio noise) is out of the sky, the radio environment is very quiet. Some scientists see that environment as such a unique resource that they propose to establish UN-managed radio-quiet zones on the lunar far side.
So far there haven't been any missions sent to land on the lunar far side. One good reason is that a lander there can't communicate with Earth unless there's a telecom relay spacecraft overhead and in view of Earth. You might do that with an orbiter in low lunar orbit, so you get brief telecom passes every couple of hours. Or you might put a relay spacecraft in a loose Lissajous orbit around the Earth-moon L2 point. Either way, this makes the mission much more expensive.
In its New Frontiers Program, NASA specifies that one of the missions eligible for consideration is the "Lunar South Pole Aitkin Basin" mission, which would involve a landing on the lunar far side. The proposal for the Moonrise mission that would have pursued that science was not selected in the last round of competition. It would not have addressed lunar sky brightness or dust lofting.
