You have JCH Optimize running on your site, which compresses and alters all the Javascript on your page. Our Autotune Error Check tool can't run all it's checks when that's enabled. If you want to run Autotune, disable JCH temporarily and verify that things are working before you re-enable it.
As to your issue, I did just try to authenticate using LinkedIn. When I did, I was authenticated and logged in properly. Can you explain more about what issues you're running into or what errors you're seeing?
Thanks,
Alex