Gox.com uses an invalid security certificate

Yes, we get it... MtGox / Gox doesn't know what they are doing. Trying to reuse certificates is not a good way get people to believe that you understand server security.

Honestly, at this point, I don't know of what they could possibly do to get their customers confidence back let alone the wider bitcoin community.

And this has been big enough of a cluster-fsck to cause the skeptical public that isn't using bitcoin to stay away from it like the plague.

Considering gox.com is not even a website yet, just a redirect to mtgox.com, and that the certificate is the same for mtgox.com... I think it's a moot point.