Thanks esmi!
It appears the problem was with my theme, which was no longer compatible with the WP core after one of the WP upgrades. It was so subtle that I didn’t notice it right away since everything appeared to work, and everything looked correct. (I didn’t even know my theme could have an affect on wp-admin pages!)
I think it was a conflict with some of the scripts, or a javascript library or something. But I upgraded my theme and now everything works like peaches! ??