GPS on the Moon
An interesting question. You'd be about twenty times further from the GNSS satellites (GPS, GLONASS, Galileo, BeiDou, JXSS) than those of us on the earth, so you'd have to deal with signals about 400 times fainter. That assumes that the GPS signals are only mildly focussed on the earth; if the antennae are sufficiently directional, it could be you'd lose even more power than that. There is also some "geometric dilution of position", the effect you can get on earth if the only satellites you can see are in a single part of the sky (used to be very common in the 1990s, when there weren't many satellites up there yet, and I think you can still get this problem in "urban canyons"). On the Moon, the entire GNSS constellation would only subtend about six degrees in the sky, so you'd always have a pretty low-grade sort of position fix.
Come to think of it... the MMS (Multiple Magnetospheric Satellites) use GPS to determine where they are in the magnetosphere, and they go fairly high up. So there must be a good bit of GPS signal that goes right past the earth and could be received on the moon.
On the plus side, there's no atmospheric effects going on (specifically, ionospheric effects). The GPS satellites transmit on two frequencies so you can compensate for this. But still, not having to worry about it at all would presumably be worth something.
I'm sure an off-the-shelf GPS unit will be confused by the altitude. (I vaguely recall some "throttling" being done, on at least some units, to make it difficult to repurpose them for ballistic missiles.) But if you're going to the moon, paying for a modified unit capable of latching on to faint signals and figuring out how the position works on the moon ought to be the least of your problems. Presumably, the MMS folks have some prior art here.