I have moved my wp-content dir out of the usual place as other devs probably have. Because of this, the somewhat hardcoded path in the add_scripts() function fails to find it and causes the AJAX functionality to fail. I suggest that the line is changed to
wp_enqueue_script('ns-mc-widget', WP_CONTENT_URL.'/plugins/mailchimp-widget/js/mailchimp-widget-min.js', array('jquery'), false);
to regulate this issue.
All the best,