I don't have this problem in Firefox, only IE (both 6 and 7).

I'm using the datepicker with a dynamic URL, i.e.
http://www.myurl.com/index.php?main_page=my_page
When selecting a date from the date picker it redirects to http://www.myurl.com/#.  The date does populate before the redirect.

I am using    

1. <script type="text/javascript">
     $(document).ready(function(){
       $("#datepicker").datepicker();
     });
   </script>
   
   
   
   

And a read-only text field for the date result:

1. <input id="datepicker" name="delivery_date" type="text">