Hi...

I ran the command Get-Mailbox -Monitoring and found that some of my HealthMailboxes are either corrupt or in an inconsistent state. 

_____________

[PS] C:\Windows\system32>Get-Mailbox -Monitoring

Name                      Alias                ServerName       ProhibitSendQuota
----                      -----                ----------       -----------------
HealthMailboxd3aa6e8a4... HealthMailboxd3aa... prep-mail        Unlimited
WARNING: The object Domain.org/Users/HealthMailboxd3aa6e8a4dd843619786dac0dee2eb0e has been corrupted, and it's in an
inconsistent state. The following validation errors happened:
WARNING: Database is mandatory on UserMailbox.
WARNING: Database is mandatory on UserMailbox.
HealthMailbox4098dbd06... HealthMailbox4098... prep-mail        Unlimited
WARNING: The object Domain.org/Users/HealthMailbox4098dbd06c13458c85cfcb3c508c191c has been corrupted, and it's in an
inconsistent state. The following validation errors happened:
WARNING: Database is mandatory on UserMailbox.
WARNING: Database is mandatory on UserMailbox.
HealthMailbox92d421caf... HealthMailbox92d4... prep-mail        Unlimited
HealthMailbox746a65a3c... HealthMailbox746a... prep-mail        Unlimited
HealthMailbox84ceac07c... HealthMailbox84ce... prep-mail        Unlimited
HealthMailbox2f9f4b8b5... HealthMailbox2f9f... prep-mail        Unlimited

___________________

What can I do to fix this

Hi,
It might very well be that you have some orphaned monitoring mailboxes that you can delete.
How many databases do you have?
You should have two monitoring mailboxes per database.

Are you on RTM?
The reason I ask is that in CU1 a new container was created for the monitoring mailboxes in the MESO Folder called "Monitoring Mailboxes". Do you have it?

Also see my response in this thread http://social.technet.microsoft.com/Forums/exchange/en-US/a00b4a97-e9d9-46fc-8c65-c5043bded183/erase-healthmailbox-accounts-can-they-be-recreat