Your SSL Certificate needs to contain all the names that you will use to access the server. See How to use SSL Certificates with Exchange 2007 for more info
If you only access it with the internal name, you should be able to disable autodiscover or change the autodiscover address to the local name and have it work. See Outlook 2007 Certificate Error? | Elan Shudnow's Blog or Security warning when you start Outlook 2007 and then connect to a mailbox that is hosted on a server that is running Exchange Server 2007 or Exchange Server 2010: "The name of the security certificate is invalid or does not match the name of for info on how to change the autodiscover name.
Since it says the certificate is expired, you should also make sure that the correct certificate is being given out by the server. Use SSL Checker - SSL Certificate Verify to verify this.
