in some cases, you can use something else instead of a div to achieve the same effect while pleasing the validator gods. for instance, a span or an img could work, and they are inline elements.
for ul li, what you can do is the following:
<style>li:hov er {background:#cc c;}</style>
<ul>
<li><a>first choice</a></li>
<li><a>second choice</a></li>
</ul>...