Jonathan,
Thanks for reaching out! Have you tried activating the default Twenty Thirteen theme to see if this issue still persists? Give that a try so we can determine if the issue lies with your current theme.
You were right on Casey. The theme we are using is loading jQuery UI directly using a script tag, causing it to be loaded twice. I posted on their forum since they seem to be loading the script incorrectly.
Great! Glad to hear you figured this one out. Since it seems like you’re all set, I’m going to mark this thread “Answered” and close it out.
We really appreciate your support and please let us know if you need anything else in the future. If you find yourself with a few minutes and would be so kind as to give us a “Works” rating or a positive star voting on the WordPress.org repo (http://wordpress.org/extend/plugins/the-events-calendar/), or even a shoutout to your followers on Facebook or Twitter, it would mean a lot to us. Thanks again for using the plugin.