This is about reading for what your writer was up to and following that off a cliff.
It is rather easy, in fact, to read the right attitude into the writer to enable yourself to ignore what, in fact, he actually did say. I have read with my own eyes a writer who maintained that it was all but proven that suspects during the witch craze were routinely raped because, of course, the records never mention any such thing. Or modern reinterpretations of Juvenal that declare that even though the work is obviously criticizing Rome -- and in areas much to be criticized, often enough -- what it's really satirizing is the stuffy old-guard who minded, in the person of the narrator.
The clearest example of it is Ovid, who wrote a solemn little treatise on The Art of Love, just as someone might write one of The Art of Losing Money to Internet Scams. Much of it was then imported, wholesale, into courtly love as perfectly serious discussion of the proper behavior between the knight and his lady love. Obvious, of course, at this distance, but many modern day readers do the same thing and are not corrected because they are surrounded by those who do likewise. (In the opening of The Discarded Image, C. S. Lewis noted the existence of such readers who like it and want only the impressions the original writer happens to make on them, regardless of his intent. And then that while he did not want to take that from them, he was writing for the other sort of reader, who want to get at the author's intent.)
The effect is strongest with fiction.
(Yes, fiction is a form of primary source. To be sure, you can't rely on the characters existing -- what a surprise -- and you have to watch out for not only fantastic element but melodramatic ones, ones that, in real life, were possible but hardly plausible. On the other hand, particularly with more modern novels, they frequently give as local color all sorts of clues about everyday life. I have heard, often, that in the court of Louis XIV, fairy tales were written for and meant for adults. Then I read an excerpt from a novel, in which a man announces he will tell a fairy tale in a saloon, and the hostess declares it's wonderful, she loves fairy tales as much as if she were still a child. Which is to say, they were used by adults with the full knowledge that they were children's tales -- rather like a motorcyclist I once saw with a teddy bear in leathers and a helmet on the back of his motorcycle. Being meant for children was perhaps part of a meta-level in using them for adults.)
Imputing irony that isn't there is the big thing to watch out of. True, people use irony, always have, always will. But many readers impute irony when they discover that the writer is saying something that they don't agree with. Dostoevsky, I've heard, has suffered particularly hard from people who refuse to believe that pious intentions can be anything but ironic -- though, no doubt, also from the necessity of the university system where people keep on having to come up with new things to say about works. To be sure, I have also seen fans imputing an unreliable narrator to works that have no evidence for that view -- even no hint -- so they can build up an elaborate alternative story that they prefer, but which has no reality to the work they are discussing.
One can also miss things that you don't agree with. John Milton -- some people argue that Satan's arguing for liberty and equality. They miss that he interrupts his own argument to point out that it doesn't annul degree and position, because he only wants to revolt against God, not have his own angels revolt against him.
And some people just choke. Shortly after Harry Potter and the Order of the Phoenix came out, I was in the bookstore, and two clerks were discussing the scene with Umbridge and the centaurs, and a little old lady customer said that she thought that the last scene of the last book would reveal that the entire series was a fantasy Harry dreamed up in his room under the stairs. She's not alone in the art. For decades, everyone took the ghosts of Turn of the Screw seriously. Then Edmund Wilson put forth that they were really the governess's delusions, and many critics followed him. One can hardly help noticing that Wilson was also the author of a review of The Lord of the Rings which had the title "Ooo Those Awful Orcs." It's kinda hard to denounce a genre with admitted classics in it, so the classics have to be forced out. sigh