To set your mind at ease look at this thread in which various TT's were tested with the platter speed app, The best was the Nakamichi, which centres the record, most of the big variation is eccentric spindle hole.
http://www.stereo.net.au/forums/index.php?/topic/49224-turntable-speed/page-2?hl=%2Bplatter+%2Bspeed#entry941503
http://www.stereo.net.au/forums/index.php?/topic/49224-turntable-speed/page-2?hl=%2Bplatter+%2Bspeed#entry941503