Is POI Offset a problem?

Was accuracy testing some different ammo, and consistently noticed this regardless of ammo (or caliber):

When bench firing on a Caldwell rest, my hits are half inch to the right of center, at 50 feet.
When firing one handed, they center in the middle. Clearly I'm doing something to shift the POI left, but if it's consistent, should I try to correct it?

Happens with .22, .38, and .45 too.

Unless you are competing with a rest I wouldn't worry about impact shift from that of the hand.  

I do find my zeros drift when I systematically work on grip and arm strength,  but it is a slow change.

Anecdote from rifle; zeros would routinely change one or two clicks from standing to sitting position at the same distance with the same ammo only because the rigidity and motion of the positions is different, even with an 18lbs rifle full of lead weights.

If you're centered offhand don't worry about it.

AMU armorer mounted a new red dot sight on Adam's pistol. He took it to the range and was sighting it in holding it in one hand same as when he shot matches. Another member said he should sight the scope using sand bags on the bench, Adam said why? I don't shoot it that way!
 Keep sights the same as you do when shooting target or matches!

Bet Shue, Zins and Henderson all said the same!

Good to know! Thanks all!