By default only integrity checks with a Severity level of "Critical" are run in the nighty scripts. All other levels of integrity checks are not run but can be enabled by request.
All other levels of integrity checks are only updated manually via the "Run Integrity Check" process from the Action menu in the record itself. To manually update all integrity checks, including Critical, use the "Run Integrity Checks" process from the Action menu on the Data Integrity homepage.
If you wish to run certain other integrity checks during the nightly processes, please submit a ticket to Veracross Support.