Hello mailchimp programmers...
in your recent plugin update I think you missed a closing div tag in the mailchimp/mailchimp_widget.php file.
See below:
</div>
</div><!-- /mc_form_inside -->
</form><!-- /mc_signup_form -->
</div><!-- /mc_signup_container -->
Note that I had to add the closed div tag before the second line in the code.
Adding the closing div tage fixed it on my site.