Okay, I'm going to tell you. But there's no proof the neighbor actually did it, so I didn't put it in the question:
There were cars scratched.
We had paint thrown on our door and windows, thrice.
We had some soapy substance thrown in our garden, that killed our plants.
There was a molotov cocktail near our fence when we came back from church on Sunday.
I don't know how to put that in there, except for the call-the-cops part...