The best thing to do is to follow this procedure:
(1) Send a copy to someone close to you that you know generally likes your work. If the piece passes this first test, proceed to (2).
(2) Revise the piece according to the comments made by (1). Any comments made by (1) are valid, since they really had to be bothered by something if they were going to even mention it. You don't have to agree, but at least look at it. Then proceed to (3).
(3) Send the piece to a critic that you know fairly well, someone intelligent enough to be able to discern your intellectual intentions (or pretensions, if you will), and versed enough in literature to be able to spot general plagiarisms. Make sure they give you a brutally honest account of their thoughts. This part takes thicker skin. Don't butter yourself up before you do it. Then proceed to (4).
(4) Revise again. See whether you disagree or agree with comments first; if the latter, edit them. If you disagree, contact the person (if you think the point may be important). Then proceed to (5).
(5) Steel yourself and send the piece to the harshest critic you know. They don't need to be a friend, they just need to be someone who's going to read this for you and tell you exactly what they think. They don't need to be as knowledgeable as (3), either. You have to make sure, however, that your piece fits into a genre they generally enjoy reading. Then proceed to (6).
(6) If you passed the test in (5), the piece is basically good to go. Make any small revisions noted, and now double-check your grammar (get someone else to do this for you if you're sick of reading it). Then put this away. For a while. As in, a few months at least.
(7) A few months later, take it out again, read it, and make any revisions you see. This piece is now ready for publication, if you so wished. Repeating the cycle again, however, wouldn't necessarily be a bad idea.
You see, after all THAT, you're STILL going to hate your piece a year down the road. At least now, however, you know others didn't hate it. That does make me feel better.