Hi,
I actually went on your website, watched the video and then tried the dropdown of the new address form and didn't had any problem selecting the country/state.
I guess that the problem is your browser. Looking at the video, it sounds like you're using a Mac. I tried on my end on your website with Safari, Chrome and Firefox with windows (I don't have a mac but a pc) and it worked fine each time.
Maybe it's a bug that wasn't yet fixed for Chrome for Mac. Do you have the latest available for Mac ?
I see that a similar bug was reported with Chrome 26:
github.com/harvesthq/chosen/issues/1138
I have the current version of Chroms which is Chrome 27 so that could potentially explain why I don't have the issue and you do (however it was also working for me before updating chrome a few weeks ago).
So far no one else reported such issue and we have thousands of users using these chosen dropdowns for months now so I'm quite confident that the problem must be on your end, especially that it worked fine for me on your website with the same browser.
In any case, we have an option in the Display tab of the configuration, which is called "Use Chosen library", and which will deactivate the chosen library which displays the dropdowns nicely. So you can turn it off if you want and that should fix the problem for you.