A factual mistake is the result of sloppy research on the part of the character, not the creator.
A character gives an explanation or quotes 'facts' that are entirely incorrect. However, elsewhere the same facts are stated correctly, and other characters call the inaccurate character out. The authors intentionally gave the character a lack of research skills as a character trait. Do we have this yet?
Hello, Unknown Troper. You'll need to get known to lend a hand here.