Your right to speak your mind is generally protected by the 1st amendment, as long as you are not threatening anybody. Your apartment complex may have regulations that you signed that restrict some of your rights to display materials from your apartment. If not, then you probably can put something in writing on your door, as long as you are not damaging the property. You can certainly write letters to them, whoever they are, to let them know that you are aware of their gossiping.
ActuallyI disagree. Contacting those fools will only encourage them in thier vitriolic attacks. Be a bigger man and ignore them. Sticks and stones will break my bones, but name will never hurt me.
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I think both answers already given are correct: absent any rules governing he placement of something on your door, you are free to post a note. However, I do not think that would help you at all in your situation. That act would just rile them up. Bullies prey on those folks out of whom they can get the biggest reaction. Ignore the best you can. Best of luck to you.
Attorney Inga Stevens is licensed in Maine. She provides general information on Avvo.com. No attorney-client relationship arises out of the information given here.