i knit cotton wash clothes (and i have even knit cotton bathmats) but rarely knit dish clothes.
But i love to knit cotton potholders from "kitchen cotton/crafters cotton/sugar and cream cotton".
i double knit these--each is double layered, completely reversable with stocking knit--in jacquard/fair isle patterns.
i am about half way through a tutorial on my blog --all about all the different styles of double knitting, and Jacquared interlocking double knitting in particular.
If you are interested in learning more about double knitting, check it out.