Problem description
I got a couple of warnings (source MSExchange ADAccess, Event ID 2937) after removing a Exchange 2007 server at the end of a Exchange 2007 > 2013 migration. The details of the warning told me, that there was a faulty value set to a attribute of the mailbox database object. Because the public folder migration was part of the migration, the error message seemed plausible.
Process w3wp.exe (PID=4652). Object [CN=Mailbox Database E2K13,CN=Databases,CN=Exchange Administrative Group (FYDIBOHF23SPDLT),CN=Administrative Groups,CN=Testing,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=testing,DC=local. Property [PublicFolderDatabase] is set to value [testing.local/Configuration/Deleted Objects/Public Folder Database DEL:4a45b7c2-10fc-42df-bdaa-82ae8a12e66e], it is pointing to the Deleted Objects container in Active Directory. This property should be fixed as soon as possible.
A quick check with ADSI Edit confirmed the message. To be honest: I made a mistake and searched for the attribute PublicFolderDatabase in the database object, but in the end I found the wrong entry as a value of the msExchHomePublicMDB attribute in the database object. It must be set to the distinguished name of the mailbox database that houses the public folder mailboxes. If you don’t have any public folders in your Exchange 2013 org, then you have to clear the value!