I've found it valuable in two circumstances. One is a barrel that fouls badly. When I first started shooting in service rifle matches, I had a military Garand barrel that would foul so badly that accuracy was visibly deteriorating during the 600 yard slow fire stage. It took hours to clean. Moly stopped that problem.
The other is long range shooting (800-1200 yards). Moly bullets typically show a slightly higher ballistic coefficient than their plain counterparts, which means a little less sensitivity to wind drift at long range. There were a number of novel theories to explain this when the data first appeared, but Walt Berger seems to have figured it out. He discovered that the lube simply makes it easier for a bullet to slip into alignment with the bore on firing. Leaving the muzzle slightly misaligned (tilted) has to be recovered from through gyroscopic stabilization. While that is happening, drag is slightly greater.
Tilt also affects accuracy, but reports on accuracy improvement with Moly have been mixed. I think this is most often because someone starts with a sweetspot load developed for a plain bullet, then simply substitutes the moly bullet, not realizing it will alter his barrel time and require him to find a new sweet spot load.
I have never seen any of the corrosion problems or other complaints the circulate about moly. I have heard that when the rush to moly was at its peadk, some unscrupuous cheap kits were produce with moly recovered from stamping operations that contained free iron. That, in turn, initiated rust. I have also run into the tendency (you need a borescope to see it) of the moly to mix with carbon and build up where the chamber neck steps down to the freebore diameter. I have also found, though, that either Slip 2000 Carbon Killer or Gunzilla will soften it and allow it to be easily removed.