Hello,
I installed your plugin today and I was surprised to land on the wp-login.php when I submited the settings form (options-general.php?page=get-recent-comments.php).
I realized it was aiming to the wrong URI. I explain: I installed WordPress as a subdirectory (I access to myblog.com/wp-admin either it's WordPress code is in myblog.com/wordpress). It's an official method.
Could you just remove the calls for $_SERVER['PHP_SELF'] ? Because of that all your forms/links aim to myblog.com/wordress/wp-admin/.
You should use the global $pagenow or deal with bloginfo('url') + wp-admin. Despite it's not beautiful, it's like that in WP until they provide an WP_ADMIN_URL constant or something like that.
Thanks a lot :-)