Ex Landlord harassing me at work

Hey Mike,
 
Thats a tough one.  However, since you know who posted the remarks if they are false you can scare the ex-landlord by threatening a slander suit if the complaint is not immediately retracted.  Otherwise, since you haven’t given too many details on the actual type of complaint, you can always protect yourself by documenting everything.  Let your corporate office know that the complaint was done by the ex-landlord by providing proof of his email address.  Remain professional and never over react to the complaint.  Even if the complaint is completely in error, you can and should keep customer service as a priority and respond by stating that you feel sorry that the individual felt the need to complain, and that you will do everything in your power to resolve the situation.
 
I don’t know if you’ve ever heard the phrase:  “There’s no such thing as bad publicity”  implying that any publicity is good, even if its bad as it gives you a chance to get publicity and to respond to the negative tone.  The same with your complaint… as long as you look like you were completely professional and did everything possible to help the complainer, you will come off as a saint and it shouldn’t impact you too much.