@Greg S. having read many of your posts I  have seen you  are a hard nosed landlord that is how you choose to run your business, glad it works for you.  

She poured cooking oil on the carpet, pulled the bathroom mirror off the wall, I'm not sure what she did to the bathroom sink but it may need to be replaced.

I'm just wondering if the dog rubbed against the walls or stairs, and even if they cleaned it, the oils or odor remained.  

It isn't uncommon to give tenants free heat(oil) in my area.

Anyone who tells you they've seen everything in this business is either fairly new to it.... or a snake-oil peddler.At the end of the day, it sounds like many of you have had bad experiences with Property Managers.... and I'm truly sorry about that.

A tenant's vehicle leaked oil on the asphalt driveway of a rental property. 

Often the trash is in the wrong can, trash in recycling, and one time oil in recycling(said auto parts store told them to do it).

People have this crazy idea perpetuated by "gurus" that investing in real estate is easy and that they should be able to kick back on the beach somewhere day 1 and just watch the rent checks roll in ... while this may be the end game, you'll need to work your tail off to learn enough and build your portfolio large enough to get to that point ... trying to bypass that hard work by claiming to be "not handy" or any other excuse is inviting trouble IMO, usually in the form of scoundrels selling snake oil by telling you what you want to hear in order to part you from your hard earned money. 

As a man, picture shaving in front of the mirror and all you have is a pedestal sink, and no place to set down your shaving cream or razor.  

I'm closing on a 1900 five-family with a relatively new oil boiler feeding a steam system.