How to add a span class in the post title?

Wouldn’t the simplest approach be to use a filter on the_title()?

function add_span($title, $id) {

    return $title .' <span class="title_span">' .get_post_meta($post_id, $key, $single) ."</span>";

}

add_filter('the_title', 'add_span', 10, 2);

This approach of course assumes you’re storing your span data as a meta value.