Hi, Everyone:
I'm sorry that it's taken me a while to respond. I was sick for a few days.
Anyway, thank you for your replies. I checked my option settings and the Quality setting in the Rendering tab was already set to "shaded." I did change the show backfacing property to on, but it still seemed to have the problem.
But what I did find is that it seems like it happens more often when I had my view render mode set to "Shaded & Wireframe," but it doesn't go completely away. And when I click off the bone, then back on, the display is normal.