Controlling the humidity in the house with a dehumidifier is a good thing and a great start. Check for any active leaks, specifically in any places where you have spotted water damage. Check for any drywall that is soft, specifically around the top or bottom of the drywall. Go outside and check the caulk around windows, the window ledgers, especially if the ledgers use any mortar, and flashing around the roof. You should take a hose and lightly spray, simulating rain and wind, with someone inside checking for leaks. Since you have a basement, look for any areas that might hold water around the foundation, check your gutters to make sure they are in good working order and the drains are directing the water away from the foundation and in a direction where the water can drain away from the house. You didn’t mention if your bathrooms vent to the outside (and not just into the attic either), if they don’t you will want to either vent them outside or include that in your dehumidifier/AC calculations. Check your dryer vent to make sure it is clean and vents outside as well.

If you can stop any leaks you find, control the humidity in the house, and wash with soap and water any exposed surfaces that may have had mold growth, I think you should be fine. I recommend you purchase some mold test kits and check for mold in the air just to be safe.