I'm currently lecturing in introductory organic chemistry; the head of the course is a very experienced outstanding teacher who (literally) wrote the book, and has won many awards for his excellent teaching. He started the course for the first few weeks of lecture. I'm covering lecture for now, and he will pick it up again later in the course (about a month and a half from now).
I messed up carbocation rearrangement today, right at the beginning of lecture. I lost 'em; they were VERY restless and chattery and obviously like "This lady does not know what she is talking about!" It actually turned out that the mistake I made was a very instructive example of a common misconception about the topic that students have, and the ensuing discussion of where I had gone wrong cleared up a lot of questions they had and got everybody to a much better understanding of the topic than if I'd just gotten it right the first time through.
BUT I am pretty sure that it is still going to kill their perception of me as someone they can trust to teach them. Every time I get anything wrong it's like another nail in my "I'm a younger female who doesn't really 'look' like a professor" coffin. I don't have any room to make mistakes, because I'm already having to prove to them in the first place that I can teach them about chemistry.
It's like a Catch-22; I end up sacrificing my dignity in a way that helps them LEARN more, but it might end up adversely affecting their learning overall if it makes them think I can't help them understand things. And it also shows up in their memories as a huge looming perception, so when it comes to instructor evaluation time... what do YOU think happens?