I'll be adding addendums for how to handle new tenants moving in (current tenant moving in a romantic partner) and who is responsible for pest infestations.

I would look for the stinkiest, flea infested hoarder house you can find.If you go the fixer upper route, forget about FHA financing. 

Then we had a flea infestation problem outside in the front and side yard.

I am now more clear on your point, but I still do not 100% follow your logic.Let me try it this way:Hypothetically...If I offer a low-income tenant a yearly leaseAnd you offer a tenant next door a month to month lease.Both tenants throw big drug-infested parties and do other unsavory things.

If they go crazy on it (maybe because more of the tree is over their property) and they cut it too much the tree can die (heck, if you are not careful in the trimming process and seal the cuts, it can also get infected/infested, end result same, dead tree later) or worse, become unbalanced and prone to crashing on your property or his - so make them aware of that.

We don't have any pest issues and the pest company stated to me over the phone that there is no infestation it's just the normal insects here and there.

Like water damage, rodents, bug, bird, pest infestations, mold...

I'm staying out of Englewood and the rough crime-infested areas in Chicago, no Harvey, Riverdale, Robbins, etc. 

I do not want to get lost in the shark infested waters of Orange County.  

It didn't work, but we still have the lady bugs.As for your problem, you very likely have an infestation of the Lady Bugs that you have not found.