Is there a place for unsignaled fallibility in fiction?

What I mean is: real people have incorrect beliefs about things, sometimes from personal ignorance, sometimes from widespread misconception or trendy falsehood. I don't mean about existential questions, but about trivialities. The wrong date for something. An assumption about the nationality of some historical figure. A facile narrative about some scientific or sociological or historical topic. A misstatement about language or art. So when a character in a fiction errs and goes uncorrected, does the error signify an error of the writer, or does it serve to more richly characterize the character and her millieu as one in which such an incorrect belief is held? Does it matter? (The basic distinction here is Watsonian vs. Doyleist, I know.)
( one example from a mystery series and two from Vorkosigan Saga fanfiction )
To conclude, I should confess what might be obvious: classical reference in particular makes me sit up and pay attention, and I like to put my pedanticism on display about it. In principle, I think that fiction would do well (and does well?) to dramatize the casual misinformation and misconceptions that float around in the world. I just started to read Plutarch's unbelievably tedious quomodo adolescens audire poetas debeat (text in Greek, Latin title by convention), but I suspect that it should give me more things to think about re: mimesis and what to do with things that intentionally or not misrepresent reality.

I mostly lurk in fannish circles but this is why I right now have a text document full of sapphics from the point of view of Simon Illyan and haven't finished my prose composition homework.

...I've been wanting this jacket for a while -- and now it's on sale! But am I really likely to wear a pseudo-Victorian jacket-y thing?

Also, I am so so tempted to buy this jacket, put silver piping and embroidery all over it, and pretend to be a Vorkosigan retainer. But I probably won't, because I am determined to be practical, damn it!