This is some great advice beeing thrown around here.
One small thing to add about being your own worst critic that works for me.
Literally think "what will they(other harsh critics) bother me about?" then fix it. Don't go like "oh I'll uhh cover it up with a shadow", no, fix it. Be honest with yourself here, if you don't find your piece to be on a "professional level" then ask yourself why it's not, then fix it. When you ask other people for critics, they should surprise you, if they come up with stuff you knew was there and have some lame excuse for then you weren't hard on yourself enough. Beat the critics to it!
I see it all the time on the forums, people receive crits and they go like "yea that was bothering me too and blah blah", then you should've fixed it before posting! That is, unless you were having a real hard time coming up with something better, but then post that with the original piece and don't wait for people to point out the obvious.
One more thing (I'm getting longwinded here). Consciously choose who you take crits from. An extreme example is the difference between deviantart and CA.org. This applies everywhere else as well. When you receive a message, always consider the source, not just the message.
"It's too bad she won't live! But then again, who does?"