As I've mentioned in another response I typically run pg_dump as follows:
nohup pg_dump {various settings} > something.log 2>&1 &
Why redirect standard error to standard out when using pg_dump? I assume that using standard out is not the backup stream.
If you want a success message in the log; write the success message to the log file if pg_dump exits successfully.
i.e.: nohup pg_dump --verbose prod > prod.sql 2> prod.log && echo "Backup Completed Successfully!" >> prod.log &
