Drupal 7 Ckeditor cannot edit profiles (picture added)
Broken unclickable fieldsets are almost always a symptom of JS not being run to build the links &amp; click events to trigger expansion. 

If the JS console is reporting errors, try to disable JS caching/aggregation, if possible, and look for offending JS errors that would stop execution. That should give you a good idea where it's coming from.

Most likely, the 3 affected sites have a similar configuration that is injecting JS which breaks further JS execution. Look for similar modules across the 3 sites. Good places to look are any custom modules, JQuery update (is it overriding the default jQuery from Drupal core?), custom blocks with JS, or any modules designed to inject ad-hoc JS snippets (I've come across sites using JS snippets despite its alpha status).