I'm willing to bank that its a jquery conflict. So I took a look at some of the code for WP UI and I noticed it's utilizing the standard $ function for jquery.
If developers are going to distribute plugin with a jquery dependency, I strongly suggest running jquery in NO CONFLICT mode as described here:
I don't know if this is really the cause of the plugin breaking my client's site or not. But if you guys will develop in NO CONFLICT MODE, it will help avoid any jquery conflicts in the future.
In the meantime, I'm not exactly sure what I'm gonna do to fix my client's problem.