I don't use wash cloths any longer on my face, but when I did I had a fresh cloth for every wash. My skin is SO sensitive that I didn't want to expose it to bacteria/mildew from a damp, used cloth.
The caveat is that using a washcloth was WAY over-stressing my skin. I believe that's what initially caused the eczema to spread to my face; I suddenly had very dry patches, and then I'd have spots with acne too.
When I backed off to only wash my face with cleanser once a day (rubbing gently with my fingers only, and PATTING dry with a washcloth or towel) and then once a day cleansing with jojoba oil on a cotton ball and then spot-treating with diluted tea tree oil where needed, my skin didn't feel so dry, tight, and sore in the patches where I'd previously had eczema outbreaks.
Just wanted to throw that out there, for what it's worth to others who have sensitive skin.