Read the stickies above and as already listed here thus far in this thread, there can be rifles with one or more issues out of box.
This doesn't mean it will not fire everytime the trigger is squeezed or will throw 12gaCylinder bore, buck shot style groups at 100meters .
Most of these rifles are very reliable out of the box as was mine with only the over-indexing issue, and lose op-rod guide. Most of the issues notsorichguy listed are not overly hard to put right yourself or in an M14 clinic by Tactical Teacher,... but again most rifles will still function with them.
The things that I would be most concerned about and are damn hard or impossible for a novice to verify especially in the store on someones new rifle are these, (1) an improperly hardened and/or heat treated bolt that could mushroom into a dangerous head space condition after a few hundred rounds, or (2) a rifle with an out of spec bolt and/or receiver lug's so as the bolt only bear's fully on one side. I saw a new shorty( CanadaAmmo Socom18) with this issue but IIRC the vendor corrected it for the owner. The soft bolt you'll only find out later not sooner so an original headspace check would be ideal and a recheck at say 400 rounds so as to show if this condition is present, but the one side bolt lug bearing issue is an unacceptable condition right away.
These 2 issues are most concerning to me for safety concerns, but are very uncommon I believe in say 99.97%, and the other typical issues most complaint's are about range from only the superficial to merely annoying, with no safety concerns, so really they are non-issues on a 400 dollar rifle that you now are aware of before you buy and have the support of an M14 community here to correct if you chose to accept this mission.
This tape will self-destruct in 10,..9,..8.......