I think blogging publicly will get you over the fear of being judged, and doing it in your real name helps even more.
But, that can be a tall order for some people. You don't have to publish everything you write. You could totally write 10 crap articles and publish 1 good one.
One aspect that I think can sometimes be troubling, is whether it's fine to just have a blog that is a miscellaneous collection of stuff covering a variety of topics, versus a blog that is about X, Y or Z at the outset. I guess this is just "the blogger trap" ( http://www.marco.org/2009/04/05/avoiding-the-blogger-trap ), but I get the impression that a blog for a specific subject would have a better reception, versus "I'm just going to write about whatever" which might have less reliability, in a sense.
But, that can be a tall order for some people. You don't have to publish everything you write. You could totally write 10 crap articles and publish 1 good one.