Wonder, I have sympathy for your situation. I am in somewhat of a similar one. We moved house last year, and the former owner did not disclose that he had had the worst relationship with his neighbours possible (we live in a semi and they are in the adjoining property). Apparently, so I later discovered, it had descended to the former owner installing CCTV and filming the neighbours doing all kinds of supposedly nefarious deeds.
When we moved in, we heard all sorts of horror stories from the other neighbours on our street, and had some fairly strong warnings. One neighbour, lets call him Mr M, told us to be really careful because a shopping directory for Mr M had somehow got delivered to our neighbour's house and their son had bought a load of stuff on Mr M's account while Mr M was recovering in hospital from a near fatal motorbike accident -- only for, when the son's ruse was discovered, the son to claim that Mr M had actually bought the items in question. From his intensive care bed. With two broken arms and two broken legs. And a smashed jaw.
Now, yes, their garden is a mess, complete with two old soggy sofas. And they have a habit of setting fire to things in the garden, like paperwork and old chairs. But my OH and I actually get on really well with their two teenage daughters, who are absolutely lovely and come round quite a bit to chat about pets and tap-dancing.
However, this did not stop me from being utterly bewildered when these very same neighbours began to dump industrial amounts of used white cat litter in their back garden and the waste land next to our garden (which is actually part of their property though my neighbour refuses to accept this). It was the waste land dumping that really bothered me because, after a while, the smell was really quite pungent. Every time I came home, I would open the car door and ... my eyes would water.
So I solved the problem in the only way I could. I went round to the neighbours wearing my most shocked face, and said "Mr Neighbour, you are not going to believe what has happened! Someone has dumped an incredible amount of used cat litter on the wasteland behind your house. When you told me people dumped there, I never thought you meant things like cat litter. Now I know you have a bad knee, so I will clear it all out and get rid of it -- do not worry about that. It smells so bad and it will attract all sorts of vermin."
And I did. And the cat litter never appeared there again. And their daughters still come round and chat about pets and tap-dancing.
A basketful of win for everyone, I think.