How do I fix my iPhone when it says cannot verify server identity?

Sounds to me like that site had an invalid certificate – one that was either expired, or completely bogus.

There is nothing you can do to "fix [your] iPhone." The problem is with the Web site, not with the phone, and the operators of the site must fix it at their end. The phone is displaying this message because the site's lack of a valid certificate means that you cannot be certain you connected to the site you think you did.

The problem isn’t with your phone, it’s with the site you’re trying to reach. The security certificate they are using is expired or invalid.