Is there a more efficient admin search function/plugin?

Altering the WHERE clause

There’s a filter named posts_search that allows to filter the SQL WHERE clause used for the query during search (when WP_Query::is_search() returns true and WP_Query->s is set):

add_filter( 'posts_search', 'wpse134392PostsSearchSQL', 20, 2 );
function wpse134392PostsSearchSQL( $sql, $wp_query )
{
    // Alter SQL clause here

    return $where;
}

Custom ORDERBY

To intercept the ORDERBY statement (for e.g. to sort by author, so the author who searches gets his posts first/last), you can make use of posts_search_orderby:

add_filter( 'posts_search_orderby', 'wpse134392PostsSearchOrderbySQL', 20, 2 );
function wpse134392PostsSearchOrderbySQL( $orderby, $wp_query )
{
    if ( is_admin() )
        return $GLOBALS['wpdb']->posts."post_date";

    return $orderby;
}

Fine grained SQL

You can as well alter the posts_clauses or pre_get_posts to return even more fine tuned results by checking inside your callback if is_admin() and $query->is_search() are TRUE.

Don’t search everything

To exclude common terms that won’t help, you can use WP_Query::get_search_stopwords() – or better: A callback on the filter. Currently the stopwords are:

about,an,are,as,at,be,by,com,for,from,how,in,is,it,of,on,or,that,the,this,to,was,what,when,where,who,will,with,www

An example filter callback:

add_action( 'wp_search_stopwords', 'wpse134392SearchStopwords' );
function wpse134392SearchStopwords( $stopwords )
{
    return $stopwords + array(
        'my',
        'your',
        'easy',
    );

}

Hint: It looks like something (a plugin probably) is already intercepting your callback as there’re words in there that shouldn’t get searched.