Now that you've found out someone needs to have their permissions cleaned out from other mailboxes

Mass Permission Removal

See what rights a user has to all mailboxes

Get-Mailboxpermission * -user domain\user.name | format-list > File.txt (for later reference)

Get-Mailbox | remove-mailboxpermission -user domain\user.name -Accessrights DeleteItem

If you just want to remove someones rights to everything, or a broken SID's rights.

Get-mailbox | Remove-mailboxpermission -user domain\user.name -Accessrights DeleteItem, SendAs, FullAccess, ReadPermission, ExternalAccount, ChangePermission, ChangeOwner

Here is the fun part, if you are doing a large group of mailboxes, you MUST finish the wizard, it queue's everythign up, so if you say Y, Y, Y, CTRL-C, NOTHING will happen, but if you Finish the wizard, the job completes

http://technet.microsoft.com/en-us/library/bb125153.aspx