Quoted:
easy way to tell if the barrel is loose, is to grab the upper reciever itself with one hand and grab the barrel at the fsb with the other hand and twist.
Bingo!!!!!
Slight movement of the delta ring and stock hand guards is normal, its the barrel to the upper receiver that you don't want moving at all.
If you find that the barrel it's self is moving against/in the upper receiver, then the gas tube will need to be pulled, the upper vise blocked up, and the barrel nut tightened one more spine index to solve the problem. The correct torque for tightening a barrel nut is Plus 35lbs, but not to go over 80 lbs. Some times you may hit the 80 mark before the top index between the spines lines up with the upper gas tube channel, and if this happens, back the barrel nut off and retighten again (may take a few times, but you will get the spines void to line up correctly in a few tries).