All right, so this glitch happened to me after I had a Plumbot that was sending love letters to somebody in my town. I ended up selling him, however, I think he got a response once I returned home because when I click "Get Mail", my character juts three squares to the right and the sound of a negative reply plays. This happens every time I try to get the mail, and the option will not go away.

Any suggestions?

Maybe you should try using the cheat code "testingcheatsenabled true". Shift-chick on the mailbox and delete it. When actual mail or bills come, a mailbox should appear somewhere on the lot. Or you can purchase a custom mailbox to take it's place after you delete it. Does this glitch happen with all sims or just one sim?

Sorry for the late response. I only have one Sim in my family, so I was unable to test it with another Sim quickly. I assume it would have the same effect, though, as the problem seemed to have been with mail appearing for a Sim that no longer existed (A sold Plumbot, in this case.)

In any case, I restored a backup of my savegame and waited for the mail to come before selling the Plumbot. Everything works fine now.