The fear of public embarrassment can be a strong motivation to think more carefully about one's ideas. Without it, I think I will more often be tempted to make a comment or post without thinking through possible ways that I could be wrong. I'd like to preserve that motivation for myself as well as others, so let's not make the cost of publicly making a mistake too low.
In this thread, "mistakes" primarily means "old mistaken beliefs" rather than "careless/foolish comments".
At a recent meetup, we tried having a structured discussion in which we would all choose to talk about a belief that influences our behavior, talk about something we protect, or talk about a mistake we once made and have corrected. And it seemed that people thought it would require exceptional bravery to choose to talk about one's mistake. Elsewhere on Less Wrong, people are concerned about retaining the ability to edit a comment expressing a position they later reconsider and think is wrong.
My first reaction to all of this is that we need a group norm so that it doesn't require bravery to admit a mistake, or to leave a record of previously held positions. My second reaction is that we do in fact have such a norm. Comments expressing a change in position, that accept counter arguments and refutations, get up voted. Old comments reflecting the old wrong position are generally not down voted for being wrong. The problem is not how we treat people that make mistakes, but that people have inaccurate anticipations of how we will react.
So, to everyone who is worried about this, I want to say: It's OK. You can admit your mistakes. You can make a mistake and change your mind. We, the community, will applaud your growth, celebrate your new strength, and leave your mistake in the past where it belongs.