Exchange 2010 to 2013 migration

I am upgrading my email system from Exchange 2010 to 2013.  I have about 2 dozen mailboxes so my 1 mail server handles all functions.  I've installed 2013 into my network and migrated a couple test mailboxes over to it.  Email has been flowing properly to and from those mailboxes for over a week now.  All mail is flowing to and from the internet through the 2010 server still.  I am ready to point my firewall directly to the 2013 server and make it the internet facing server.
So my questions:  from what I've read, once I point my incoming email directly at the 2013 server, I need to create a new UCC certificate with the same FQDN I'm currently using (mail.mydomain.com) on the 2013 server and move my remaining mailboxes.   My mobiles using activesync should not need to have anything done - they should pick up the change at that point - is this correct?  The desktops on the domain will automatically pick up the change as part of the move process - that is simple.  I expect certificate errors on the desktops until the UCC cert is created.  Anything else I need to be thinking about?