I fixed the error, for now, but like thegraphicscompany, I’m trying to remember how as well. I think I just turned off the option to “hide” other shipping methods when using free shipping, and that seemed to do it.
Thinking about the way the internal logic of Woocommerce works, when there are no alternative shipping methods displayed and free shipping is assigned by default (or by coupon), the cart doesn’t recognize ANY shipping method as being selected.