When we signed our lease we were not allowed to have any pets (I wanted a rental with no pets) I assumed that the renters next to us had the same rule.

Remodel your units to be tenant/ pet proof. 

If it is me I'm keeping the tree and putting down pavers with proper drainage underneath, the only exception would be if you have a pet and/ or allow pets in the unit.

The town closed the case and the inspector seemed pretty irate with with them because they had never complained in all the years that they lived there and they filed this complaint after their order to vacate.I found out that they had two dogs in the unit and I am tempted to take it out of their security deposit since they were not supposed to have pets.

Just any general pet peeves would be helpful :)

Even then...ehh.Pets are optional (unless they're ADA-approved), so if you aren't a fan of pets, don't allow pets.When dealing with repairs:If you can, provide the other tenants with a list of handymen to call for all possible issues.

If there are pets in the unit, make sure they have food and water on a regular basis (Purina), and if they are abandoned contact these people: https://www.nokillnetwork.org/d/Massachusetts/(Or you could keep them for yourself if you want--they sure need a new home)Good Luck!

I have the advantage of being pet friendly though so I basically shoot fish in a barrel.

Also currently have a no pet policy, but try to keep an open mind depending on situation. 

I try to avoid pets whenever possible, I presume your state allows a fee for pets, my experience is the deposit is never big enough.