Hmmm this may or may not be the culprit, but your current markup for the mega menu DIVs contains extraneous data that shouldn't be there:
<div id="drop1" class="mega solidblocktheme" style="width:200px">
<div class="column">
<ul>
<li><a href="/about-library/staff.shtml">Staff</a></li>
<li><a href="#">Friends of the Library</a></li>
<li><a href="#">Support the Library</a></li>
<li><a href="/about-library/bod.shtml">Board of Directors</a></li>
<li><a href="/about-library/history.shtml">Library History</a></li>
</ul>
</div>
</div>
The "columns" DIV shouldn't be there, as all your drop down menus are simply single file ULs, not multiple columns of ULs. Try changing the above to:
<div id="drop1" class="mega solidblocktheme" style="width:200px">
<ul class="ulmenu">
<li><a href="http://www.javascriptkit.com/cutpastejava.shtml">JavaScript Clocks</a></li>
<li><a href="http://www.javascriptkit.com/cutpastejava.shtml">JavaScript Scrollers</a></li>
<li><a href="http://www.javascriptkit.com/cutpastejava.shtml">Text Effects</a></li>
<li><a href="http://www.javascriptkit.com/cutpastejava.shtml">Password Protecting</a></li>
<li><a href="http://www.javascriptkit.com/cutpastejava.shtml">Form Validation</a></li>
<li><a href="http://www.javascriptkit.com/cutpastejava.shtml">Ajax Scripts</a></li>
<li><a href="http://www.javascriptkit.com/cutpastejava.shtml">Image Effects</a></li>
<li><a href="http://www.javascriptkit.com/cutpastejava.shtml">Link Effects</a></li>
</ul>
</div>
This simplification should be done for the other mega drop down DIVs on your page as well.