It depends on piece by piece. I've bought name brand fabrics from the LQS that after washing were unacceptable. Recently I'm working with some fat quarter scraps from Walmart and Joann, and I was surprised to find how much I liked working with the Waverly fabrics at Walmart.
I look for a good feel, that depends on the person. I look for a good tight weave, except that I also work with homespun fabrics and would consider many of them unsuitable if they were a dyed print instead of a woven. I look for good printing, those registration dots on the selvedge should be perfect. I also smell my fabric, some have dyes or processes that emit odors that bother me, so it might otherwise be usable to someone else but not to me.
I try to keep the fabrics I'm using to a similar weight, often hard to do with my scrap style of quilting. But batiks in general have a terrific tight weave and I enjoy working with them, but I would consider them too lightweight in many cases.
Old saying: you can't make a silk purse out of a pig's ear. Some fabric is just not worth my time to use and so I get it out of my stash.