A public mistake followed by a public apology often causes people to think better of you than they did before.
Yes, one year I made a lot of stupid online mistakes. My students would contact me, I'd fix the mistake, and apologize. In spite of my mistakes, I got great student evaluations. They noted that I was sensitive, kind, responsive, etc. No one mentioned my mistakes.
Now, I'm not saying go and make mistakes on purpose. But when you do, take correcting them as an opportunity to show that you're a good person.
You know, Melba, I had a similar semester a few years back. (I was really stretched thin with Mom-care and teenaged-kid care/drama and just plain teaching too much.) I don't think I posted ANY document without at least one or two typos, screwed-up due dates, or the like. Like you, I fixed things, sent out a message saying, "Oops, screwed up AGAIN, thanks for catching it! Signed, Your Friendly Fumble-Fingered Prof," and moved on.
Like you, I got great evals that term. People get it, and I think it does make us more real to them (not that I intentionally try to make mistakes like this--they just happen!).