To eek out the most in accuracy from your M14-type rifle, fire a magazine or two from your rifle after it's been disassembled and assembled again. This will seat the receiver / barreled action into the stock.
ETA: This is why I don't bother to field strip my M14-type rifles after shooting them. Clean the bore with wet/dry patches, make sure the bolt raceways are properly greased and be done.
Also, some brand new M14-type rifles tend to become more accurate as they're "broken in". The bolt lugs often "wear in" and make better contact with the receiver after firing a few rounds through the rifle.
As always, I recommend the excellent drop-in Sadlak Ind. NM op-rod spring guide, which has shrunk groups in my rifles by about 1/2 an inch. YMMV, but others here have experienced the same improvement.
Finally, some factory ammo produces better groups than others. I really like American Eagle match ammo loaded specifically for the "M1A". The LRBs i've had built really like it.
Claude from RA parts has extensive experience building M14-type rifles when he was associated with Armscorp. His statement to me about M14 accuracy was that a properly built standard issue rifle should print about 1.5 MOA groups or so with quality non-match grade ammo such as US M80 ball (DODIC A166).