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.
Followup to: Don't Fear Failure
In the same theme as the last article, I think that failure is actually pretty important in learning. Rationality needs data, and trying is a good source of it.
When you're trying to do something new, you probably won't be able to do it right the first time. Even if you obsess over it. Jeff Atwood is a programmer who says Quantity Always Trumps Quality
The people who tried more did better, even though they failed more too. Of course you shouldn't try to fail, but you shouldn't let the fear of it stop you from tyring.
I wouldn't go as far as to say that quantity always trumps quality, but where the cost of failure is low lots of failures that you pay attention to is a pretty good way of learning. You should hold off on proposing solutions, but you also need to get around to actually trying the proposed solution.
I'm normed such that I'll spend more time talking about if something will work than trying it out to see if it works. The problem is that if you don't know about something already, your thoughts about what will work aren't going to be particularly accurate. Trying something will very conclusively demonstrate if something works or not.
Note:
I originally had this as part of Don't Fear Failure, but that post got too long.