Its definitely true that nobody notices/minds a mistake unless you emphasise it by letting it affect the rest of the song. I used to sort of panic & tail off - or my voice would 'wobble' a bit after a mistake & so the mistakes stood out like sore thumbs. Now I just smile & carry on as if it didn't happen, so the focus moves away from the mistake immediately & it doesn't have time to settle into the listeners' conciousness.
Amoret (daughter) sang with her own guitar accompaniment for the first time in public on Sat night, and I was amazed how calm she was. She made a few mistakes on the first number, but did not appear at all flustered and just corrected herself & carried on. I know she made mistakes, but I can't remember what they were - but I certainly would have remembered them if she'd panicked noticeably.
I would recommend the old crib sheet idea, except I've gone off that a bit since Amoret & I sang a whole song back to front because I put the two sheets of paper in the wrong order! It made little sense sung that way - but again nobody noticed - the sad fact is that people aren't actually paying that much close attention usually.
Which isn't necessarily a bad thing. We were discussing various singers the other night & I moaned that X always sings the same songs - Amoret felt it didn't matter at all because X sings in such a lovely relaxing way that you can float off & think about other things - which she thinks is part of the appeal of that singer.