urmachtra and Triple P are talking about the same problem.
When you are connecting over HTTPS, the plugin strips away all the scripts queued for embedding. jQuery, Prototype, etc. are no longer there. Since the plugin itself relies heavily on these libraries to work, it breaks down pretty fast, i.e. the "Edit" translation link.
I've narrowed it down to the new Scripting Guard feature, introduced in version 1.9.21. Earlier versions should work OK over HTTPS. If you want the latest version, you'll have to deactivate Scripting Guard. The simplest way I've found is to comment out lines 2680 to 2684 in the main PHP file:
/* add_filter('print_scripts_array', 'csp_filter_print_scripts_array');
add_action('admin_enqueue_scripts', 'csp_start_protection', 0);
add_action('in_admin_footer', 'csp_start_protection', 0);
add_action('admin_head', 'csp_self_script_protection_head', 9999);
add_action('admin_print_footer_scripts', 'csp_self_script_protection_footer', 9999);
wp_enqueue_script( 'thickbox' );
Hope this helps someone, and hope Heiko will find the time to fix this. Cheers!