In Chrome (Version 31.0.1650.63 on Ubuntu Linux 13.10 64bit).
I just tried logging out of WordPress Admin and it works fine. Log back in and it breaks again.
So from my point of view, it is fine as no one will be signing up to the mailing list if they are logged in to admin. You may wish to investigate further though, as other people will probably want to test their form whilst still logged in to admin. It could be some odd combo of plugins and theme code of course. I didn’t build this site, I’m just updating it, and it is a bit of a mish-mash!
For reference, this is on WP 3.8, has a theme based on Flipbook and has Contact From 7, Easy Post Types, Really Simple Captcha, Scissors Continued, Shadowbox JS and Simple Image Sizes plugins, in addition to MailChimp for WordPress Lite.
Thanks for an excellent plugin and very speedy support response.