A.F.
To M. it sounds more like a personality issue rather than self-esteem. Some personalities are very focused on quality and doing things correctly while others are more up for the challenge of trying something new.
I really don't think it's an issue of self-esteem or confidence and trying to focus on those things won't do a ton of good. She hates to be wrong in front of people, which means that she probably normally feels she's right. (I also bear these awesome traits...)
I'd focus on the specific situations and her feelings about those situations. In a situation where she wants to try something new but is afraid of doing it "wrong," J. talk her through what she would do, what she thinks could go wrong, what she thinks will happen/people will say if she does it wrong, how she reacts when people around her do something "wrong."
Also, remind her that there are lots of ways to do something. J. because she doesn't do it the same way as someone else doesn't mean her way was "wrong." That's a big lesson that I'm still working on learning.
I think always trying to help her put herself in other's shoes (if she's afraid of being rejected, find out how she would feel about another little girl who "put herself out there" in the situation at hand) and helping her to think through her feelings and reactions will be immensly helpful as she grows up.