I have the classic external Mopar 2 post mirror - 1960's.

The head of the mirror is a little loose on the ball and moves when I drive my car.

What can I do to fix this problem?

Thanks, Peter

Peter, Check to see if the glass is held in place with a snap ring.If it is remove it and the glass comes right out.Inside you will find a screw that may have loosened tighten those screws and see if it is better.If the glass is glued in it most likely will break. I had a local glass shop make me one for about $5.Most all I have seen is the snap ring type.
Mopar Action magazine had a blurb about this and said that they drip super glue into the ball socket and don't take them apart(the glued in glass). They also wrote that the super glue will fill the void tightening the ball socket and will still be adjustable.I have never tried the super glue trick.

Great! Thank you for your suggestion.

Regards, Peter

Let us now what you find

My single post mirror was glued in. Soaked it in laquer thinner and it loosened the glue up and the mirror came out in one piece. Did not damage the chrome at all.