If she insists on paying you cash, then she needs to hand it to you, so that you can in turn write her receipt for her records.Tenant #3:   Sounds like she's trying to negotiate the rent without actually saying so.    

But, the reason I'd require it, would be to insist on that loss of use rider and their personal property coverage, so when they look at me in fear and I say, "No, we don't pay for that," before they can start crying, I can then say, "But, that insurance you got WILL pay for it."

The tenant insisted on moving out, so the owner agreed to let them out of their lease without having them sign anything.

You need to insist that dogs be on leash at all time and fully under control of the owner.

All great insights already here Winn, but if you are able to oversee the painting, there are some ways to help with this often unavoidable turn over expense....For example, this time insist on some high end paint (think specialty paint store or the very best big box stuff); try a pearl or washable finish; I like one color for all the interior of all my units, ideally a white that can hide some imperfections (know and keep the code); this means no color or matching mystery later; then on the next turn over, see if you can't get away with just a wall cleaning; use a damp sponge mop with tsp or a tsp substitute  (and then rinse it with a clean water and a damp sponge mop)..not too much water, just damp.. 

If you insist on owning a SFH, which make for poor rental properties, you should do as my son does.

I insist on addressing anything that wasn't clean to avoid them coming back later and using it against me.

The tenant insists that her mom is not staying with her and just comes over a lot to help her with cooking and cleaning.I believe the reason she doesn't want to add her mom is parking. 

We request an inspection contingent deposit but the seller insisted an as-is offer.  

But, it's your job to insist :-)