was the mildew only where the clothes were? if so i would guess that the mildew was on the clothes which happened to be making contact with the wood. Best thing to do is set it in direct sun for a while (if you have any )
I haven' t had the best of luck drying clothes on racks for similar reasons. They have to spread out alot and you can't create a "cave" with clothes. hanging on a line gives plenty of air circulation. I Only dried my clothes this way when my dryer broke. It was only a short time because My dh clothes came back in from the laundry line dirtier then when he threw them in the basket ! he figured a new dryer could be worked into the budget after that. I'm spoiled with the soft ,non dusty or pollen laden or animal hair and bird poop covered clothes. Darnit, those commercials with the little kid playing hide and seek in the clothes on the line and the happy mom shaking out towels and folding them were a bit misleading
oh! I just pictured them in room temp/outdoor situation. hmmmm. I could go crazy with ideas on a woodstove drying rack......picturing something hanging from the ceiling.....circular , on tracks like a rack in the dry cleaners jsut for fun ..... oops sorry I guess I'm starved for achievable projects.