Reader Rich Love describes an issue with Mail (that he has seen reported by other users, as well) where Mail does not delete mail messages from the POP server if a mail rule "deletes" one of the messages automatically on your Mac:
"If you have a rule set up to delete mail [and have your mail preferences set to remove mail from the server 'right away'], and a message matches that rule, mail will be deleted on your Mac but will NOT be deleted from the POP server. [The problem has been hard to track down because it only happens] when an email comes in that matches your rule. If you receive 50 emails and just one of them matches the rule, none of those emails will be deleted from the pop server."
This type of rule is common for users who set up rules to automatically delete suspected spam messages. Rich provides a workaround for the problem: instead of setting your rule to delete such messages, set the rule to move those messages to the Junk folder, and then manually delete them later. With this modification, Rich reports that mail is deleted from the server as expected.