So it it was a dead tree you complained about then you have a case. 

There is an old Chinese proverb that says "When is best time to plant a tree?

One of the very big trees in one of my rental properties in katy texas fell in the front yard.

The best time to plant a tree is 20 years ago, the 2nd best time is today.

Even if the tree sits on their side of the property you are free to trim the trees that overhangs on your side of the property any way you like.  

They take the guts out of it where they shoot it, and then strap it onto the trunk of the car or in the bed of their truck and take it back to their house, and hang it upside down from a tree limb to let the blood drain out of it for a certain amount of time.

It sounds weird, but a vase filled sticks or small tree branches from around the property might be a nice touch on an empty table or counter. 

Mainly, because structural issues can be a complete black hole of money, time, effort--and it can be very difficult (and costly) to anticipate just how much money, time, and effort they'll consume.First, you'll need to figure out what's causing the structural issues--it could be settlement at the footers caused by ground water, it could be wood rot or termites in a beam, it could be masonry degradation caused by water coming off the roof, it could be improper drainage of the roof, it could be tree roots degrading the foundation, it could be a plumber who cut out a critical joist to install a line 20 years ago, it could be improper construction, it could be any or all of those things, and it could be any number of other potential causes.

That off-marketing deal finding stuff is not my cup of tea, personally. 

Other cities seem to embrace it....think Myrtle Beach Area, A1A area, Smokies, Joshua Tree, Ski Resorts, Branson....probably almost every national park is overwhelmed with visitors the past few years.