Given that there seems to only be two articles that are listed as falsely reported as misinformation (the Reason article and the BMJ article also mentioned in the Telegraph report from today), I have to assume that there actually aren't that many large errors on the part of the fact checkers. If there were more than two or the mistakes were much bigger, then the free speech advocates would never stop mentioning it.
There can definitely be bias when it comes to fact-checking, I wouldn't deny that. I also think that education and knowledge sharing can be greatly harmed by social media incentives to provide the most "engagement". Having an actual human in the process somewhere introduces some error but also cuts down on a lot of the dumb crap that would otherwise spread.