There is such problem, indeed. It is caused by the conflict with Prototype.js that most of Page Editor, including designer and debugger uses. It can be simply worked around by overriding the $-function by calling "jQuery.noConflict()".

<script type="text/javascript" src="/js/jquery-1.2.6.js"></script>
 
<script type="text/javascript">
 
var $j = jQuery.noConflict();
 
 $j(document).ready(function() {
 
 });
 
</script>

More about that on the jQuery website