I have reopened the previous issue MOD-10296. Apparently this has shown it's head again in the 1.9.2 branch.
After upgrading to 1.9.2, the following issue has appeared in our Moodle site:
Under Internet Explorer (both 6 and 7), visiting the Edit Profile tab while viewing a user profile causes the browser to complain loudly and sometimes crash. It partially loads the page and then pops up a box saying that the page contains both secure/unsecure items. Clicking on either the 'Yes' or 'No' options causes it to pop up another error dialog that says
Internet Explorer cannot open the Internet site https://moodlesite/user/editadvanced.php?id=3&course=1
The browser then redirects to an internal IE error page. This same page works fine under Firefox, and it also works fine under IE if you manually change the change to http:// instead of https://. Disabling https:// would be an acceptable workaround for now, but there doesn't seem to be a way to independently change it without also disabling it on the login.