I faced issues, in which the remember me plugin did not work properly.

Steps to reproduce the issue

Login in Joomla Site, check "remember me" checkbox. Wait until the session expires.

Expected result

User is logged in independent of port (SSL/no-SSL).

Actual result

If you log in in SSL and switch over to non-SSL, you are not logged in after the expiration of the session.

System information (as much as possible)

PHP-Version 5.4.36-0+deb7u3
Webserver nginx/1.2.1
PHP-Interface for the webserver fpm-fcgi
Joomla!-Version Joomla! 3.4.0 Stable [ Ember ] 24-February-2015 23:00 GMT
Joomla!-Plattform-Version Joomla Platform 13.1.0 Stable [ Curiosity ] 24-Apr-2013 00:00 GMT

Additional comments

I worked out a patch, which works independently of the server port.

Open: /plugins/authentication/cookie/cookie.php
Function to edit: onUserAfterLogout
Before:

    $this->app->input->cookie->set(
        $cookieName, $cookieValue,
        time() + $lifetime,
        $this->app->get('cookie_path', '/'),
        $this->app->get('cookie_domain'),
        $this->app->isSSLConnection()
    );

After:

    $this->app->input->cookie->set(
        $cookieName, $cookieValue,
        time() + $lifetime,
        $this->app->get('cookie_path', '/'),
        $this->app->get('cookie_domain'),
        false
    );

Open: /libraries/joomla/user/helper.php
Function to edit: getShortHashedUserAgent
Before:

    return md5(JUri::base() . $uaShort);

After:

    return md5($_SERVER['SERVER_NAME'] . $uaShort);

This solution works independent of using http/https. I can do a PR if you think this change is reasonable.