I recently had questions about this, and indeed adding https to everything removes the IE dialog box about mixed content.
However, another problem arises: If all links are now https, when a user clicks on one of those links (such as those found in the navbar or footer), isn’t the user going to a page with non-https links, and consequently throwing the message again? I tested this, and yes, once someone clicks one of those https links, the IE message reappears on normal pages.
Is there anything that can be done to avoid this, without having to tell visitors to disable the warning in IE (I never assume they will)?