THE GOOD PART
I have been shooting moly coated bullets for many years. I moly coat them using the NECO kit and method. Most bullet manufacturers use the same or similar method.
Typically, a barrel will need 20-30 moly coated bullets to be fired before it is adequately seasoned. Once it is seasoned you will not need to season it again. Normal bore cleaning does NOT remove the moly coat in the bore. Actually that was some shooter's complaint; you can not get the stuff out too easily. If you want to remove moly from the barrel two things seem to work reasonably well. Either use JB bore paste or similar semi-abrasive cleaner or just start shooting naked bullets which wears the moly away. A combination of the two worked quickly for me.
I like moly coated bullets in my high volume rifles, mostly varmint rigs. While there have been many wives tales about moly bullets, most of the facts are now known. I have shot many thousands of moly coated bullets in both custom barrels and factory barrels.
I have never experienced moly build up in any barrel. Moly bullet use will allow you to shoot very long strings of fire without the need for bore cleaning. Some of my custom barrels do not allow copper to build up at all. However, that doesn't mean that the rifle bore shouldn't be cleaned. I'd guess that "moly build-up" may result from cleaning a bore at unreasonably long intervals. There may be other causes but I have never experienced this problem so could only guess what would cause this.
Generally speaking, moly will not increase or decrease the accuracy of a rifle. Naturally, any change in a load will likely result in some change in group size but moly does not lend itself to moving a group in either direction. An accurate load can normally be found with or without moly. Inaccurate rifles do not become accurate with the use of moly.
IMO, Moly can allow for a small increase in velocity given a load of equal pressure. Because moly is a very effective lubricant it will reduce bore friction and result in a slight decrease in velocity until the load is adjusted. However, with a small increase in charge weight, the velocity will be restored and can even be enhanced. This has been my experience with several cartridges.
As to the issue of moly attracting mosture - this is another problem that I've never experienced, if it even exists. It may be that most of my barrels are stainless steel or that I use normal bore cleaning/lubricants but I have never had a problem with regard to moisture or rust in any of my rifles that shoot moly coated bullets.