Well, I'm not an aspiring writer but as an amateur musician and visual artist I can say that I can generally tell when my works are not as good as I would like them to be, and I can generally guess ahead of time which pieces will have a better reception among my more critical friends.

In addition; I know a couple of aspiring writers and if anything I would say that they are often very self critical and judging by what they have openly shown me against what they have reluctantly shown me I would say that they did indeed have a good sense of what was good and what wasn't.

Based on my experiences, I would say that it is fairly common for artists to have a fairly accurate awareness of their own shortcomings; whether or not they can successfully ascertain a workable procedure for overcoming them is a different issue.