LP's: the measure of off-centre record spindle holes ?

Cleeds is right slaw. The feedback signal is taken from the platter not the record. 
If it bothers me I take the record back and get another copy.

Points taken. They make sense. I was hoping it would be an added benefit over and above. Thanks guys.

I usually notice this audibly, especially with piano or sustained strings, and it drives me nuts!

If not too bad, a workaround is to slightly enlarge the center hole with a reamer tool and reposition.  Do this away from the turntable and carefully brush away any vinyl scraps.  Return the record to the turntable centered by eye on spindle and hold in place with a reflex clamp.  Note where tonearm has greatest excursion from center, lightly mark the direction on the label with pencil (or post-it style flag).  Remove clamp and push record against spindle at that location to correct, and re-clamp.  Sometimes a few iterations are needed.  Next time you play the record, you can just look for your pencil mark.

Important:  The eccentricity not correlated between the the two sides, so this process needs to be repeated on the other side.  Usually the production hole is well centered in the vinyl, but somehow the master with the grooves wasn't aligned when pressed.

As ghsmd implies, it can be a tricky business to correct for off-center vinyl. For one, if you widen the vinyl's center hole it could drive you nuts to accurately place the record in the proper spot. I just don't have the coordination or the eyesight to pull something like this off.  Plus, how much time do I want to devote each time I wanna listen to my old Surfin' Bird single?

@gshmd,

My brother.