I opened mine up as well Elroy, and seeing no way to actually fix the loosness in the ball and strap, I drilled the rivets out. I then took the ball retainer strap and flattened it out a bit. Took some scotchbrite to the ball. Fitting the ball and strap back together, I then tried to thread some small self tapping machine screws down into the drilled out rivet holes.

I failed... The screws would not take in the pot metal, so I then drilled right through the mirror to the outside. Used two small machine screws with nuts on the inside with locktight to cinch the strap tight against the ball.

You see screw heads on the outside, but she's super tight now! Kind of cheesy, but I think you wouldn't notice unless you were a mirror expert.

Having now read the wobbly mirror post, I think 66Beau has a good fix with the center punching fix.

Don't laugh...