There is no reason a Rem 700 in 30-06 should not shoot MOA or better. I would suspect that the problem lies with the scope, the cleaning of the bore, loose action screws or a loose trigger nut.
Next time you head to the range, get someone else (that shoots well) to shoot the gun for groups. If they have a problem then start digging.
If you know a reloader, get them to load two dummy rounds for you, without primer or powder. Mix the two dummies with two or three loaded rounds. Load them all in the magazine and shoot for group. This is a sure check for a loose trigger nut. 
Ed
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