Have removed the <p></p> tags and replaced with a div, this work fine with <blockquote></blockquote>.
I don't know why this is, just seems the <p> and <blockquote> won't play nicely together, perhaps it's because they are in a <li></li>?
$comment = preg_replace('/\[quote\](.*?)\[\/quote\]/ims', '<blockquote>$1</blockquote>', $comment);
$comment_item .= "<li><span>$comment_date<br/>$comment_time</span><div class=\"comment_detail\"><strong>$commentator</strong> $admin_option<br />$comment</div></li>";