Hi Henrik Schack,
Firstly thank you for the excellent plugin. I wanted to report a small error I found and a fix. I discovered the notice because I was working on some styling for the login screen and I installed your plugin on my dev environment to see how the styles looked with a third field on the login screen.
The error message:
Notice: get_userdatabylogin is deprecated since version 3.3! Use get_user_by('login') instead. in D:\wamp\www\wordpress\wp-includes\functions.php on line 2841
Line 171: $user = get_userdatabylogin( $username );
Line 171: $user = get_user_by('login', $username );
Hope that helps, thanks again for the awesome plugin!