I just upgraded my MacMini Server from Lion Server to Mountain Lion using OS X Server. I am having the same problem with PostgreSQL that I did last year when I first instal
File permissions are restrictive on the Postgres db owned by the Mac OS. These permissions are reset after reboot, or restart of Postgres: e.g. serveradmin start postgres.
So, temporarily reset the permissions or ownership:
sudo chmod o+rwx /var/pgsql_socket/.s.PGSQL.5432
sudo chown "webUser" /var/pgsql_socket/.s.PGSQL.5432
Permissions resetting is not secure, so install a version of the db that you own for a solution.