You should resolve to take better care next time, and evaluate where your mistake was, but I don't see how shame helps anything.
Getting singed helps avoid hot objects. Shame helps avoid stupidity.
I disagree--perverse incentives. If I was ashamed every time I was wrong, I might be more careful. Or, I might stop admitting I was wrong. I make an effort to congratulate myself for admitting I'm wrong, for this reason.
Now that I think about it, it would be even more helpful to find out which of these I would do.
This is our monthly thread for collecting these little gems and pearls of wisdom, rationality-related quotes you've seen recently, or had stored in your quotesfile for ages, and which might be handy to link to in one of our discussions.