Upgrade of Wordpress' media search function to find matches in the filename which is stored in the GUID column. In the end, a much more user-friendly (client-friendly) experience. Works with modal select windows too (ex: add media buttons).

gistfile1.txt

/* Upgrade the Media search to allow for searching the filename.
* =========================================================== */

add_filter( 'posts_search', 'guid_search_media', 10, 2 );

function guid_search_media( $search, $a_wp_query ) 
{
    global $wpdb, $pagenow;

    // Only Admin side && Only Media Library page
    if ( !is_admin() && 'upload.php' != $pagenow ) 
        return $search;

    // Original search string:
    $search = str_replace(
        'AND ((', 
        'AND (((' . $wpdb->prefix . 'posts.guid LIKE \'%' . $a_wp_query->query_vars['s'] . '%\') OR ', 
        $search
    ); 

    return $search;
}