My newest property has a "damp basement" no obvious leaks or puddles but after the last heavy rain in Dayton the basement was quite damp. my thoughts are fill in cracks DE humidify clean and seal and paint. some black mold forming. upstairs completely dry no sign of mold etc.What should my next step be?

A lot of furnaces have a humidifier on it.

. , I'm guessing you acted quickly and were able to find dehumidifiers, I was at work and by the time I got out it was such a mayhem and I still can't find humidifiers anywhere unless I travel way out of my area, luckily only one house didn't have a dehumidifier and a friend let me an ancient one but it works!

Same thing in the unfinished basement, GFIs are needed down there, except for the single outlets the sump pump and humidifier are plugged into. 

I will use good old common sense and start with the humidifier, as I have been both on the roof and under the crawl space and know there are no issues there.     

We had a toilet at our rental overflow (not exactly sure why yet) but it's caused around 6k worth of damage.The disaster clean up company we're using has a de-humidifier that is making the rental over 90 degrees inside.What kind of compensation would be appropriate for the tenant? 

I also offered to buy silicone ice trays2) sprinklers don't water the lawn evenly causing certain area saturate with water: repaired3) basement shower head occasionally dripping water: repaired 4) master bedroom ceiling light/fan turned on by itself at nights: repaired5) gas fireplace flame is smaller than optimal: ignored6) water accumulating on window wood sills: turns out they set humidifier at 60% indoor causing condensation7) Kids bathroom toilet water tank - slow water intake: repaired8) unused rifle bullet found on the sidewalk - tenant was very agitated: I went to the sheriff's office and was told it's hunting season and someone probably dropped it. 9) Washer making loud metal banging noise. - Manufacturer attempted to repair three times and eventually I managed to get a new washer under the warranty, but the delivery was such a headache because tenant refused to let us in if they were not home.

Forced hot air also heats the air up too much and makes it dry, thus making a need for a humidifier. 

I just paid $7000 cash for new 95% 100kbtu, 3.5 ton 13 seer AC with humidifier.

My humidifier that is connected to my furnace knocks for some reason.