True, the "One Ring" probably sits pretty high up on the magic item power level.
From Treasures Of Middle-Earth:
Invisibility, which is not broken even in combat, because the Ring draws the wielder deeply into the wraith world; this makes him invisible to all earthly eyes, but brilliantly visible to those at home in the wraith world, such as the Nazgûl; the wearer naturally also gains the ability to see those things which are invisible.
So, yeah, a bit more than your average invisibility. How the wearer casts a shadow while wearing it should be quite impossible based on that description, but then, I guess, Tolkien needed it as a storytelling element.
Or maybe it's the second part of the rings description, he can see things that are invisible, therefore he can see his shadow.
Who knows, I don't base any of my RM spells on LotR anyway, as it's such a different kind of setting when it comes to magic.