I recently tried forcing https in the htaccess file and noticed that the relationships in the main contact screen disappeared. They show up if I access them through a listing on the dashboard, but if I access the record through search they are simply not listed. Also the dashboard doesn't display properly and can't be configured. I haven't noticed other effects of https but they may exist too.
The first thing I'd check is whether your
civicrm.settings.php is set without the
https and if so, change that. Then flush caches and test again.