When redoing this house the two themes I would like to stick with for this home are durability and ease of cleaning.  

Are the walls and carpet clean?

The existing mold problem is almost certainly caused by the downspouts dumping water at the foundation, something we will address immediately after closing, but we saw a puddle of water in the middle of the floor, plus water around the perimeter of the basement. 

You can often get houses like these at a pretty substantial discount compared to the flips that have freshly painted agreeable grey walls and laminate floors.

Second, I already have one rental property 3 streets over from this one which has never had a vacancy and only minimal repairs (less than $400 annually for system check-ups and cleanings).

It is 6 units condo complex. 3 units at 1st floor and 3 units on 2nd floor, they are all 1 bedroom 1 bathroom, 693 sqf. gated.

So far they seem to be receptive when I send a notice to clean something up, but everytime I check on the place, there's something outside that looks awful.

I'd assume I probably wouldn't want to send a crew of people to work on a meth house without having it cleaned up first, even if it was being gutted anyway. 

They left the items there for about two months and paid a $500 clean up fee for the items left behind.

If I have had a tenant for more than 2 years, I generally don't worry about broken leases especially if they leave it clean.