This happens on all my "secure" pages, such as Login, My Account and Checkout.
When I click the Log In link as a customer i get prompted with the security prompts stating:
"This page contains both secure and nonsecure items.
Do you want to display the nonsecure items?"
"Page contains unauthenticated content"
"connection partially encrypted"
That indicates that somewhere in your templates or stylesheets you have hard-coded actual URL links to http://xxxxxxxxx instead of using relative paths to objects.
This can also happen if you have added banners with http:// links and not told them to skip display on SSL pages.
You can identify most culprits by searching your browser's View Source for:
Then work through your template files and stylesheets and remove those hard-coded links. If they are caused by click-tracking scripts somewhere, try converting them to https:// links or contact the vendor for assistance with alternate scripts.
Basically, *never* hard-code a full HTTP:// URL into any page/template/stylesheet on your site unless you know for certain that doing so will not produce this sort of error. This is especially true for <IMG SRC=...> and <SCRIPT SRC=...> tags.
Sometimes these same errors are caused by images mentioned in your stylesheet. Double-check to be sure that all those images actually exist. If they don't, then they'll produce "404 Not Found" errors, and sometimes that'll create a "loop" to attempt displaying a 404-error-page, which can in turn throw even more messages.
And, if you have created a "custom" 404 page, then if *that* page has any missing images referenced on it, or on its stylesheets, you could end up in a loop that not only throws security/encryption errors, but also creates excessive traffic in your hosting account, which will make your hosting company unhappy.