There's obviously something interfering with Facebook's Javascript file, but I don't know off hand what it is. If it works when you change the template, it could mean:
1) The template itself is causing the conflict
2) A module that only shows up in that template (due to different template module positions) is cauing the problem.
To diagnose, you'll have to narrow things down further, as I don't know your site well enough to know the problem, and I don't see an obvious cause. To narrow things down, when you go to that page with the another template enabled, do you still see the problem?
If not, then try to determine any modules that aren't showing up with the different template, and try disabling them with the 'live' template. See if it still doesn't work. If not, there's something with your template that's conflicting, but again, I don't know what it is.
You can do the same tests on two pages with the same 'live' template, since it sounds like you're only seeing that error on Video pages. Figure out what else is different about the working and non-working page and try to disable those differences.
If you can narrow it down to a specific module or plugin that's causing the problem, that will help us come up with a solution.
Thanks,
Alex