Symptom: Form javascript is output to the html inside the #newsletterwidget-n aside element, then it is output a second time inside the div.newsletter element.
Reason: It is included in the get_widget_form function on line 14 of widget.php, then it is included a second time on line 111 of widget.php just before get_widget_form() is called.
Solution: Comment out line 111 of widget.php