Once it has been cut from the wheel, the usable life will be a few weeks maybe a couple months max if properly stored. While it may not mold, it will desiccate and become hard and waxy. You might not be able to tell if you're just grating it finely, but if you're cutting off slivers it will taste different when it's been sitting for too long in the fridge.
Local Italian and gourmet groceries sell it for about the same price as Costco. The advantage over Costco is that you get it cut from the wheel in whatever quantity you want, in front of you and you're not buying it as shrink-wrapped wedge.