Will installing an OSB floor in the attic create moisture problems?
Nope, it shouldn't cause problems with moisture buildup -- but how much blown in fiberglass do you have up there? If it's less than your roof joists, it's not enough, and you should think about adding some (or a lot, actually) to bring you up to R-30 at the least in your attic.

If you do have that much up there, but you moved some to the side to put down the OSB, you committed a minor home improvement sin and you should pull up the OSB, put down some 2x6's crosswise to your rafters, and then put the OSB on top of that.