When I got Miles in June, I was so worried about this issue. I live in an apartment complex, with neighbors above, below, and on both sides of me. Miles had really, really bad separation anxiety for the first couple weeks I had him, and would bark whenever I left...every day for work.
So I decided to get to my neighbors before they could get to me. I put on my happiest, friendliest smile, and went door to door with Miles, and told them the situation. I told them that if they ever had an issue they felt like they needed to bring up with me, to call me personally, and gave them a card with my number. It's really funny how it worked. I never heard any complaints (and I KNOW he must have been annoying in that first week or two). When I have talked to any of my neighbors since then, some of them will admit that they heard him, but they'll just shrug it off and say that it was "no big deal". I have a feeling that had I not made the first move, the situation could be different (with noise complaints, etc).
I know how mad you must be (I have dealt with anonymous messages before...so immature)...but maybe it would help to kill them with kindness. Talk to your neighbors and tell them there was an anonymous message left, and ask them straight out if they've had any issues with noise from your dog. Explain that you don't want to be "that" dog owner, and that you really want to know if his barking is disturbing anyone. If someone speaks up, be super friendly and talk it out. If they don't, then it's their fault for not bringing it up to you. After all, it's really hard to leave a nasty note on the door of the sweet little girl with the cute dog.
