Hey there,
So I copied the text from above like this into the advert widget:
<div class="AW-Form-1379976796"></div>
<script type="text/javascript">(function(d, s, id) {
var js, fjs = d.getElementsByTagName(s)[0];
if (d.getElementById(id)) return;
js = d.createElement(s); js.id = id;
js.src = "http://forms.aweber.com/form/96/1379976796.js";
fjs.parentNode.insertBefore(js, fjs);
}(document, "script", "aweber-wjs-2bhvmzz4g"));
</script>
The error of just showing a script text went away, but the form still does not show in the side bar even after clearing the cache.
Does it happen to show for you?