Display Postgres server output in terminal and record to logs at same time
Just use tail -f /path/to/log and you'll be able to see the log contents in a terminal as well. You can use a terminal tool that can "monitor for activity" if you'd like to be notified when something happens.

A more complex solution would be to set PostgreSQL to log to rsyslog, and set rsyslog to log to a tty as well as a file