I never handle them once on the screens . the more u handle them the more chances to break them. I've never seen mold. But as long as there's not a lot of humidity u shouldn't have to worry. I use a fan to circulate the air around.
If you put them on window screens and don't pile them up (just a single thin layer with a little space between roots) there is no need to turn them.
I take mine off the screens just prior to going to sell them and place them in brown paper bags. I keep some select roots for my own consumption and hang on to those for up to a year, eating some here and there. I still have 4 roots left from last years batch and they still look great. I put one in my blender on grind for a couple minutes and then put it in a little fancy glass that I keep on my home office desk and eat some just about every day.
I have never had any problems... but now good air flow and low humidity are very important.
If you were trying to dry them in a outbuilding that had a leaky roof or in a damp basement or anywhere that you had higher moisture levels - you could definitely have mold/fungal problems.
I use the same method. I have a 3 foot square wood frame with window screen. Lightly wash the dirt off the roots, then place them on the screen for drying inside the house, away from sunlight windows. If the weather outside is low humidity, I open the windows to help with airflow. If the weather is humid, I keep the windows shut, and turn on the ceiling fan. Once they are on the screen, I don't tough them again until I am ready to sell them.