Material affect on health and safety of occupants (I) infestation of insects, vermin or rodentsI called the day after to try and get out of the contract due to the infestation.

An infestation might lead to a health hazard and, who knows, they may send an official to check and see whether the issue is hazardous, forcing the owner to handle it.Good luck, that’s a very nasty problem and it seems as though you’ve handled it to the best you could on your own.

The tenant has access to backyard (not in lease but offered as a freebie) it's in decent shape with not trees or plants whatsoever but my neighbor's back yard is lush green and some of his plants creep into the backyard.There will be occasional uninvited guests such as Centepedes and Beatles when the tenant opens his door.Now they are asking me to call in for an exterminator,the previous tenant never once mentioned it to me.Its not an infestation so I think it doesn't require me to call for an exterminator,it's not an infestation per se.How do I handle this demanding tenant?

While there is tons of money to be made in our Seattle market, it's a fairly shark-infested market when it comes to cash offers and finding value. 

We replaced flooring, window treatments, painted the interior, made major upgrades to the termite infested exterior, and more.

DO NOT waiver on checking them out because ive seen some pure roach infested slobs in some of my inspections..

I couldn’t even imagine the power that tenants could have if they wanted to make a fuss out of a mouse infestation, even though this is a very common issue in multi family (especially in our neck of the woods, I dealt with this myself last year…) and you have done everything in your power to try to counter the problem.

The inspectors from the pest control company did not discover this infestation under the bricks on the walkway to one of the units.  

(btw I don't know how hogs are in Michigan, but here every Oklahoma county is considered "infested" so we get free reign all year to go hog-huntin'!)

Even if you have a secure network, your tenant's PCs could be infested with malware, viruses, etc. that cause problems.