I have only used moly in .41 mag. It required more powder to bring a bullet up to speed. It could be pushed faster than wax-lubed before it started to lead. Lee Alox allowed the same increase in speed. If there is a little leading in the barrel prior to using moly bullets, I can imagine ( I don't know) that it would affect accuracy. Doing a chemical clean job prior to using moly bullets would maybe ( again - I don't know) ensure a slick sliding bore.
When an autoloader bullet is being chambered, the tip of the lead touches, then slides a short way along the chamber. If there is a lube streak left, it gets hammered into the case as it expands on firing. This little streak of lube and burned lube seems to make the cases dirty unless I clean the chamber occasionally. I can imagine a little buildup of moly doing this also in an autoloader.
Oh - I have used moly in a 30 06 and a 300 mag also - accuracy was fine, but the Hornady bullets had no sealer coating on the surface, so the moly ends up on everything. They too required more powder to push them up to speed.
On the upside, the moly will lube the case neck as it slides in, likely ( again I don't know for sure) making a more consistent chamber pressure on firing.