I think there are many ways of handling this, so I'll share what I've settled on for now in the profiles I manage. Even though I'm a relative newbie, I've come across this kind of thing a lot because of the number of US immigrants from non-English speaking countries in my heritage.
I have started creating a "Research Comments" section beneath the "References" section specifically for this kind of commentary. Two places where you can see examples of this are:
https://www.wikitree.com/wiki/Pysh-4
https://www.wikitree.com/wiki/Makar-22
As you can see in both of the above examples, I'll simplify the narrative in the main part of the profile (and in the data fields for the person) by writing the correct information (to the best of my ability to ascertain), but then I will call out errors in records, errors in the transcription from the written record to the database, and so on, as bullet points in the "Research Comments" at the bottom.
My main motivation for doing it this way is that I hope it will be helpful to other people who are trying to research the person (or their relatives), without muddying up the main profile for people who just want a summary of facts related to the person.