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
I got this error after my computer froze and rebooted on its own. The solution for me was not found on this page, rather on another very highly rated SO question with the same error psql: could not connect to server: No such file or directory (Mac OS X). The answer: just delete this file /usr/local/var/postgres/postmaster.pid, then brew services restart postgresql did the trick. Heed the warning on the linked answer about killing postgres processes before doing this else you could corrupt your db permanently.