WARNING: Exchange 2013 RTM CU1 changed the behavior on where MonitoringMailboxes (HealthMailbox<Guid>) are created. In RTM, they were created in the default container for the Root Domain (usually, in the "Users" container). In CU1 they are created in the "Exchange System Objects/Monitoring Mailboxes" container.
This causes an issue when removing Mailbox Databases: when a HealthMailbox connects to ActiveSync to test searchive health, a subcontainer is created for their pseudo-ActiveSync Device. When removing a Mailbox Database, the Exchange Trusted Subsystem attempt to delete the mailbox, but fails. This is because the Exchange Trusted Subsystem DO NOT have the "Delete Subtree" permissions in this container/user objects.This causes the Cmdlet to issue a warning that the Mailbox Couldn't be deleted.
Shame...
One possible resolution (I haven't tested yet) is to grand the DeleteSubTree permission to the ETS group on the Monitoring Mailboxes container and apply to user/inetOrgPerson objects.