I ran across this today with a customer.  We were setting up Exchange UM to connect to Lync and while that was working just fine, users could leave voicemail messages for other users, the email messages weren't being delivered to the user's mailbox.  Looking at the Application Event Log on the UM Server we say the following error message:

 

Log Name:      Application
Source:        MSExchange Unified Messaging
Date:          2/11/2013 11:22:08 AM
Event ID:      1423
Task Category: UMCore
Level:         Error
Keywords:      Classic
User:          N/A
Computer:      SERVERNAME
Description:
The Unified Messaging server encountered an error while trying to process the message with header file "C:\Program Files\Microsoft\Exchange Server\V14\UnifiedMessaging\voicemail\8e22c540-bc77-4f72-9a60-758a04a1522b.txt". Error details: "Microsoft.Exchange.Net.ExSmtpClient.TlsApiFailureException: A TLS API failure occurred. Error = 0x80090301

 

The TLS API failure was being cause because they had applied KB931125 to the server.  You can read more about this issue from the Windows Server Blog.  Unfortunately this causes the Trusted Root Certificate store to grow rather large and thus causes the TLS API failure.  The fix is to either delete any unneeded root certificates or run the Fix it from KB2801679.