I had this posted in the Links forum, but I have done more research and found that it is a universal problem on my portal.  When I click on any action item on a module it makes all of the other modules on the page (with the Initial Visibility property set to "None") show a broken image icon on the right end of the module header.  So for example the behavior would be reproduced if I clicked on the printer icon at the bottom of an HTML/Text module, or if I clicked on the ellipses link to the right of a link in a Links module.  It seems the resulting round trip causes this broken image icon to appear.  Modules which have their initial visibility property set to "Maximized" or "Minimized" don't seem to have this problem.