Microsoft Exchange Information Store service encountered a corrupt AD object

m_krone 

Identify what kind of mailbox it is, they are. It is likely they will be orphaned "In-Place Archive" HealthMailbox.

Get-MailboxStatistics -StoreMailboxIdentity <Mailbox GUID> -Database <Database GUID>

Then, remove it:

Remove-Mailbox -Database <Database GUID> -StoreMailboxIdentity <Mailbox GUID>

Automatically identify mailboxes:

(<Mailbox GUID 1>, <Mailbox GUID 2>, ..., <Mailbox GUID n>) | ForEach-Object {Get-MailboxStatistics -StoreMailboxIdentity $_ -Database <Database GUID> | select DisplayName}

Automatically remove mailboxes:

(<Mailbox GUID 1>, <Mailbox GUID 2>, ..., <Mailbox GUID n>) | ForEach-Object {Remove-Mailbox -Database <Database GUID> -StoreMailboxIdentity $_}

EDIT, P.S.: I had the same exact errors and was able to eliminate them.