On the demo site you linked to, I can click the links on that page using Chrome. There are some issues with a few of Facebook's social widgets right now, and I wouldn't be surprised if you're experiencing some of them.
Can you try updating the SCLogin parameters for "Login Button Type" to "Image" and then use the Image URL setting beneath that to link to a picture you'd want to use of the Login button? You can simply take a picture of the Login button already on your site and upload that image to your server so it looks the same as what you have right now.
That will skip using Facebook's Javascript buttons, which again, are having a few different styling issues right now due to a Javascript update on Facebook's end of things.
Let me know if that helps,
Alex