Nice design btw... really like this site.
I've checked the code and unless you've actually added the shortcode twice I think the most likely cause is some jQuery which seems to be coded into the page. Check point 5 on the FAQs page which explains about jQuery conflicts in more detail and offers some info about how to resolve it.
What I would recommend is this:
1. Do the usual steps to try to isolate the error (like turn off all other plugins, try temporarily activating twentyeleven theme etc). I think this will give you a bit more information about what the problem might be.
2. Use a jQuery consol to debug... I can see there's several errors coming up that are unrelated to the audio plugin so its possible getting rid of these will fix the conflict
3. Go through your theme and make sure there is no hardcoded jQuery at all. I have a suspicion there is - that it is fancybox JS that is causing this... see the last section of code when viewing source (lines 252 downward)
Let me know how you go and hope this helps