Make sure all parts on your rifle are tight (barrel to reciever, action, gun to stock, etc.). Then check the bases and rings. Is the crown damaged? Is the BAR bedded or free floating?
Remington and Savage are both good guns.
Everything seems tight except for the forearm piece. It wiggles some but from what I've read it's normal and I don't really see how that would make a difference in how it shoots. Everything else is tight and the crown seems to be fine. No rough spots that I can tell and feels smooth if you run a q-tip around it.
How do I know if it's bedded or free floating? Not sure what exactly that means.