The scope will need to be refocused slightly when you change power. I'm not sure why. I've never looked through a Celestron spotting scope, but I find their binos to be way overpriced for what they are.
To figure out the kind of power you'll want, take the size of the object you're looking at (.308 bullet holes, I'll assume) and multiply it by the power of the scope (Let's say 60x). .308x60=~18.5. Can you see an 18.5 inch object with your naked eye at 600 yards? Or if you prefer, you can divide the distance by the magnification: 600/60=10. Could you see a .308 bullet hole with your naked eye at 10 yards?
That being said, magnification isn't everything. Resolution is important too. The ability to pick up small details (like bullet holes) will be greater in a higher end spotting scope.
Good Luck.