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Don't just rely on W3C for validation as it doesn't catch all the closing tags. I've even seen it miss a missing HTML tag and closing li tags etc.
Sounds normal: in HTML (not XHTML) the HTML and closing li tags are optional. :) You can get in to trouble, however, with tables with missing
</td> or </tr> tags - again, these are theoretically optional in HTML (so the problem won't show up when validating) but especially old Netscape browsers can have big problems with this: Firefox mostly has this fixed but you should always use them to be sure.