if your dog does not bark they have nothing to complain about. Now if your dog is big and gets out they have reason to bitch. People are just either dog people or not. Lucky for all, all our neighbors have dogs in their yards and they barks as dogs do and no one cares at all.

So to annoy neighbors: buy huge speakers and install in vehicle, drive it around and have it go "boom boom" at 2 in the morning. Target shoot cans in the yard with a BB gun or their cat.
Have stuff delivered to their house by UPS that your order online such as sex toys and such. The wife or husband might or might not enjoy that. Send a letter to the wife or husband from imaginary girlfriend/boyfriend stating the love for him or her (typed). Put up many christmas lights and tacky decorations such as deer and leave them in the yard for 3 months after christmas.
Send them brownies with laxatives anonymously or flowers with pepper and the list goes on and on.....the trick is to be subtle.....
Get a second dog that is bigger and "scarier" such as a bully breed and they will STFU for real cause you will sick the dog on them for reals. That;s how we do it in the USA...