wp admin - Is there a quick way to find out what posts haven't been tagged? in WordPress

I think this could get resource-intensive quickly, but fastest API way would be to create list of tags and query for posts that dot belong to any:

$tags = get_tags();
$ids = array();
foreach ( $tags as $tag ) $ids[] = $tag->
term_id;
$posts = get_posts( array( ag__not_in' =>
 $ids ) );

If you have large amount of tags or need to do this often it is probably better to look into building raw SQL query for this.