999, good story.
Should we be striving for perfection? Probably, but attaining it would be counter to the real nature of the music, not to mention impossible. It's a fact that those imperfections resound on multiple listenings out of proportion to their actual significance. It's always good to get other opinions, even if you don't heed them.
Sometimes, I think, those mistakes become an integral part of the experience of the song, and because they "stick out", break the predicted progression and become something that draws you in. Case in point is on a song we talked about here some time back, "I saw Her Again" by the Mamas and the Papas. When Denny sings the first line of the chorus (I saw her) after the second orchestral signature after the bridge, I defy anyone to sing along without singing his mistake.
This doesn't work for flat notes and sharp notes as well obviously, because the tonal clash conjures that cringe feeling. My guess is that the more you record, the less flat or sharp you'll be, but you'll never ever get past that phenomenon where you say "damn, I really sounded great on that take except for that one line! You have three options then. Re-record the whole thing (and have the problem recur elsewhere!), record a second track and patch in the line (sometimes works, though there seems to be an organic unity to a single take that is often lost when you "frankenstein" tracks together). Or live with it until it stops grating on you. I do think, however, you will always hear it. My guess is that even Joan Baez has to deal with that.