Display a tag only if there is a description

The object returned by get_tags() should have a description property, so you don’t need to try to get it again. Just check to be sure $tags->description isn’t empty. You should probably also reorganize so that you don’t do anything at all unless if($tags). Thus:

// Get ALL the tags!
$tags = get_tags( array( 'hide_empty' => false ) );
if ($tags) {
  foreach ($tags as $tag) {
    if ($tag->description) {
      echo '<dt><a href="' . get_tag_link( $tag->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $tag->name ) . '" ' . '>' . $tag->name.'</a></dt><dd>' . $tag->description . '</dd>';
    }
  }
}