What is a good way to verify that a restore completed successfully in SQL Server?
It is considered good practice where I work to run DBCC CHECKDB after a restore, especially if the backup is of an unknown quality. 

CHECKDB will at least tell you if your DB has any consistency errors, and checks the logical and physical integrity of all the objects in the specified DB.

A similar thread is on ServerFault: https://serverfault.com/questions/187869/should-i-run-dbcc-checkdb-before-full-backups-or-after