I work for a publication that runs reviews. We received two requests from authors that we did follow up on:
1. The author accused the reviewer of misinterpreting something in a way she found very insulting. The reviewer did not intend to insult her; I believe it was an honest mistake (poetry isn't literal, so misreadings happen). We ran a correction nonetheless because it seemed like an important point to get right.
2. The author said the reviewer had spoiled an important late development in her book. We apologized and redacted the offending sentence online. Now, I think there's a margin of error when it comes to what is and isn't a "spoiler," and again, the reviewer wasn't trying to be malicious. But I sympathized with the author's concern that her fans might read this spoiler and be upset.
We made these corrections/ redactions because we provide edited content that we hope people will see as having some authority. But review sites are a whole different thing. They aren't edited or curated, and anyone who reads them should know to take them with a grain of salt or ten. I've seen attacks and errors there, and I simply put no stock in any review that reads like a rant. I hope any thoughtful reader would do the same. I actually like that these sites present unfiltered public opinion and leave it to me to decide whom I believe. I wouldn't especially want to change that; I think there's a place for both curated/edited and unedited reviews in this world.
When the comment rises to the level of personal libel or threats against the author, I dunno. That might be a case where mods and/or lawyers would get involved. But just getting things wrong? It sucks, but it happens. I've read movie reviews where famous professional critics didn't seem to grasp the basic plot of the film. Criticism is opinion, dependent on one person's interpretation, which can be limited. In the Internet age, with hundreds of wildly differing reviews at our fingertips, that should be all the more clear.
That said, I don't think I'd read my own Goodreads/Amazon reviews. I might have someone else screen them for useful info/feedback, but that's it. There are things authors don't need to see, and reviews (at least good ones) are written for readers. If a reader hated my style and characters and just wants to sound off, perhaps garbling the plot in the process, I think that's their right. Hopefully other reviews will counterbalance them.
ETA: This opinion could be influenced by my experience teaching literary classics to college students. Many of them hated and/or misunderstood books that I loved. It annoys me when people won't give a book even a fighting chance, but again, it happens. We all start from different places as readers. I don't think Toni Morrison feels gravely insulted when college freshmen dismiss her books as "depressing" or "immoral" or completely fail to grasp what she's saying.
When one reviewer alone wields enough clout to kill a novel's sales based on a misunderstanding or malice, I can fully understand the author's anger. But how often does that happen, especially on a review site?