You need to specify an ID for the first argument. I used the submit buttons as naming conventions until the plugin author corrects it.
// register_sidebar_widget('Most Favorited Posts', 'wpfp_widget_view');
// register_widget_control('Most Favorited Posts', 'wpfp_widget_control' );
wp_register_sidebar_widget('wpfp-widget','Most Favorited Posts', 'wpfp_widget_view');
wp_register_widget_control('wpfp-widget','Most Favorited Posts', 'wpfp_widget_control' );
and
// register_sidebar_widget('User\'s Favorites', 'wpfp_users_favorites_widget_view');
// register_widget_control('User\'s Favorites', 'wpfp_users_favorites_widget_control' );
wp_register_sidebar_widget('wpfp-uf-widget','User\'s Favorites', 'wpfp_users_favorites_widget_view');
wp_register_widget_control('wpfp-uf-widget','User\'s Favorites', 'wpfp_users_favorites_widget_control' );