Validating your page when using nested list items requires proper tag structure. It seems obvious but it can be difficult to spot.
The correct structure for lists is as folows
<ul>
<li>item</li>
<li>item</li>
</ul>
Which looks like this.
Now if you want something like this.
Heres the code.
<ul>
<li>item
<ul>
<li>sub item </li>
<li>sub item </li>
</ul>
</li>
<li>item</li>
</ul>
Note that for the sub item list that you have to nest it within the <li> </li> tags.
There are other ways of doing it to get it looking right on the webpage but none of them will validate. If your tags have a valid structure the chances are it won't cause problems in other browsers.
See this page about closing tags.