They use my yard as their bathroom.  

I make note of homes that have newspapers piled up on the porch, high grass in the yard or grass growing in the gutters. 

He gave Noah the blueprints, saying: "You have 6 months to build the ark before I will start the unending rain for 40 days and 40 nights.”Six months later, the Lord looked down and saw Noah weeping in his yard - but no ark.

If you made your "buyer" responsible for maintenance, yard, etc, then it could work.

In fact, we keep up the mowing, etc.Yes the tax lot # is listed, the sellers agent sign was in the yard of the house, with what ended up being our Agents name and number listed.  

You'll also want to set up some house rules because technically, you are renting out a room and they have access privileges to the common areas like the kitchen, LR, FR, laundry, yard, etc.

There are commercial products that can kill the root of the tree and not harm the rest of your yard. 

I'm trying to improve the property as the current tenants have stuff all over the yard.  

You could look for other indicators, I was listening to a BP podcast the other day, I'm sorry I don't remember the number and the guest was talking about his best performing mailing lists and he liked owner-occupied high equity owners, he also suggested going onto craigslist and looking at the yard and moving sales listed in your area, get the address and find out if they are owner occupied.

Since there was a small amount of dog poop (we'd been there the week before, with 1 small dog, in a tiny yard, like 30x15), the landlord did need to pick up the remaining poop there.