In Change Auditor 6.0, viewing Private searches which are enabled for Alerts is not easy. There is not GUI interface to view this, unlike 6.5+. In some cases, upgrading to 6.5+ may not be possible.
The following query can be used to identify all searches currently enabled for alerts:
SELECT * FROM ChangeAuditor.Query.Def WHERE CAST((ChangeAuditor.Query.Def.QueryXML) AS NVARCHAR(MAX)) LIKE '%alert-enabled="true"%'