Thank you for your methodical suggestions. I have discovered the culprit. There is apparently some complex interaction going on with the Popular Posts Tabbed Widget and the length of the post. If I make the post longer (or the widget shorter) the issue resolves. This may also be affected by the quirky way 2013 handles the sidebar/footer overlap.
I've temporarily resolved the problem by moving the footer content to the sidebar and don't intend to pursue it further. I'm overdue for a redesign anyway. WP was supposed to make life simpler, I swear, one day I'm going back to hand-coding html and using tables for layout. You kids get off my lawn.