This is more a suggestion than a support thread, but I noticed that the admin area was saying one file - loadingAnimation.gif - wasn't being loaded over https.
Tracing the issue backwards it looked like the path to the image was being got through an includes_url() call.
In lib/WordPressHTTPS/Module/Filters.php, there's already the line:
add_filter('bloginfo_url', array(&$this, 'bloginfo_url'), 10, 2);
Adding the almost identical line:
add_filter('includes_url', array(&$this, 'bloginfo_url'), 10, 2);
straight after it seems to fix the problem without any other ill effects.