Strangely, it probably is normal. I had one briefly and I recall that idiosyncrasy.
Thanks, Raul. I thought I was losing my mind here. There's a little set screw on the underside of the tonearm, where the arm tube joins the pivot (this is the joint that is "floppy"). Perhaps by tightening that set screw the joint will straighten and become stiff, if you will pardon the expression. (Sorry, could not resist.)