I can't remember anything that was a straight-up factual error. There was something along these lines from a private tutor my parents had to hire to make up for too many days I missed one semester due to health problems. One day when we were covering evolutionary biology she goes, "Well, I don't believe in this, but I'm obligated to teach it to you." Doesn't inspire a lot of confidence, but I appreciate the candor. Which reminds me of the time in middle school a girl in my class said her grandmother believed dinosaur bones were put there by the Devil and the teacher had to give an awkward response to that.

There is one common misconception among English teachers that I think everyone has heard at some point, the difference between "effect" and "affect" being different parts of speech.