Yoga, no matter which way you look at these occurrences, there is no doubt that there is sure to be some future history between your next door neighbours and you. My advice to you is:- (i) Keep a closed mouth (ii) Don't concede your entitlements (iii) Where necessary, make notes of any occurrence or anything that looks like an occurrence (iv) Two wrongs never made a right (v) Don't get sucked into something you want to stay out of (vi) If there is a battle situation, don't fight unless you think you can win (vii) Consider installing some unseen cctv camera if things don't improve (vii) Have your camera phone ready at all times to record anything you think should be recorded.
Try to contact the previous owner of your house. Some enlightenment might be provided to you. No harm in talking to some existing neighbours also, you might pick up something regarding your next door neighbour's behaviour.
I had a neighbour from hell once. His wife and he were dictators and whenever they got somebody to listen to them in their aloofness they'd say "We're a different kind of people to the Lepers, next door"and other stuff as well. They were right, they were different and slowly but surely I wore them down by saying nothing and doing less. Both of them are old now and depend on us whenever something happens. The assistance is one-way i.e. from us but no matter I am what I am and they are what they are. I like to think I'm amongst the lepers that gave thanks.