While opening the Public Folder Console on a Exchange 2010 you get following Error:
Error:
"Multiple MAPI public folder trees were found. It was running the command 'get-publicfolder -getchildren -identity '\' -server '[Exchange 2010 server name]'"
Cause/Customer scene:
This was in a 2nd Exchange install environment with that customer. (2003 > Cloud > Back 2010 internal [2003 removed])
The customer had internal Exchange 2003 then swapped to some cloud solution and because they found out that the provider does read all their E-Mail and the "NSA" also they wanted to have it back internal away from the unstable cloud. Well not enough someone who does not understand public folder importance de-installed the Exchange 2003 and forgot the System Folder (He exported the PF with Outlook.exe and deleted the regular PF's) while de-installed the Exchange 2003 (Dead Objects where removed and he could Deinstall clean) but the PF-Structure was still there. Happened before and comes back with all Migrations.
Here is how it looks WRONG in ADSI:
This green is the object leftover from Exchange 2000/2003 which makes the problem.

Now before! You change anything in that direction without MPSS (Microsoft Support). You use NTBACKUP/Windows Backup to make a backup of the Domain Controller (No not your Netvault/Bexec/acronis/disk2vhd/netapp snapshot) AND you do a LDAP/LDIF export of the object you want to handle on a Domain Controller.
Here is how to export the OBJECT:
Get the DSN Name on the wrong Object > Right click and Properties:

Sample: "CN=Public Folders,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=customer,DC=local"
Replace that string with yours and run the command on a domain controller:
ldifde -f D:\edv\Falscher_PF_2003.ldf -d "CN=Public Folders,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=customer,DC=local" -p subtree
This will look like this:
dn: CN=Public Folders,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=customer,DC=local
changetype: add
objectClass: top
objectClass: msExchPFTree
cn: Public Folders
distinguishedName:
CN=Public Folders,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=customer
,DC=local
instanceType: 4
whenCreated: 20051221122036.0Z
whenChanged: 20140318134543.0Z
uSNCreated: 10385
uSNChanged: 2416062
showInAdvancedViewOnly: TRUE
adminDisplayName: Public Folders
name: Public Folders
objectGUID:: Jg2/uZHE+0eQDPOXnbZgow==
systemFlags: 1610612736
objectCategory:
CN=ms-Exch-PF-Tree,CN=Schema,CN=Configuration,DC=customer,DC=local
dSCorePropagationData: 20140319124713.0Z
dSCorePropagationData: 20140318134543.0Z
dSCorePropagationData: 16010101000417.0Z
msExchPFTreeType: 1
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Then after you check all you delete the Object:

After that reboot the Exchange and all should be fine

Endnote:
Here in general how to Export/SYNC/COMPARE Schema Version (Even in Multi Forest Enviroments)
http://technet.microsoft.com/en-us/magazine/2009.04.schema.aspx#id0180006
To export the schema from the source forest, do the following:
- Log on to a member server or a domain controller.
- Open a Command Prompt window.
- Type the following into the Command Prompt window:
ldifde -f PRODSchema.ldif -d CN=Schema,CN=Configuration,DC=WS08DOMAIN01,DC=local
- Press Enter.
Figure 1 shows the output you'll see from this command.