Side to side play is acceptable. Not alot, something probably around .125". It should still feel tight while moving it from side to side. The oil pressure should take care of it. I think the in and out play is bad, but not 100% sure on that.
hello; It seems when questions come up on turbo acceptable specs there's nothing really cut in stone. I bought a used turbo on this site and it's newly rebuilt and there is play. I forget the in and out or the side to side ammount but the seller says the movement will be taken up when there's oil running thru it.
IBBY