If you think that "grep -E 'ERROR:|WARN:' pg_dump_$DB.log" is insufficient, then write a script to get MIN(), MAX() and COUNT(*) of each table before you do a pg_dump. After pg_restore, run the same script, but pointed at the new database.
SELE the "first" (presumably ordered by primary key) and "last" records
Backup and restore I mean during downtime only. I wanted to double check what all things we need to validate after a successful restore. Like table count , all 14 objects count, first and last row of important tables, row count of each table like dat?