Symptom
Local mailboxes no longer work as expected.
Note: A "local" mailbox is one on a UNIX-style operating system that allows users of the same computer to exchange messages without sending them through an email server. Earlier versions of Mail had an option in Mail Preferences for "UNIX Account" that you could use with this type of local mail. This should not be confused with the On My Mac mailbox.
Solution
For new messages, send to local users as you would anyone else, via an email server.
An option you may consider for preserving this feature is to set up an IMAP server on the computer. IMAP is an included feature of Mac OS X Server 10.2. Though it is also possible to achieve IMAP service on the standard (non-server) version of Mac OS X, Apple does not provide technical support or instruction for this.
Note: If a local mailbox was present at time of the upgrade, it will have been moved to On My Mac. However, the mailbox no longer receives local mail.