reading through the documentation, it appears that it modifies all http:// urls to
https://. many sites on the web do not support the https protocol on all their pages. Those that do offer port 443 access may only be encrypting the content with a server based key... meaning that they did not purchase a certificate, they generated their own. You would normally need to add a Trust-Exception to your browser to view these pages without warning popping up.
HTTPS-Everywhere seem to support a white and black list for site to include or exclude the urls from being rewritten as the page loads. It may be a little bit of work to configure to your browsing habits...but should not be too far off from the default included lists.
One thing to note... If you have your browser autocomplete forms, including remembering account names and passwords... these may break, since your browser probably will not save these setting while on a secure page.