If you notice one particular flaw in an author's fact checking or reasoning, to what extent do you discount the rest of what that author claims?
If you hold a narrative view of other's actions--X did Y because she is a Z--then you will tend to assume that the author is a liar and cannot be trusted.
But truth-seeking, like any other human tendency, is on a spectrum. (A psychopath is at one extreme, while Abe Lincoln, god bless his honest soul, held down the other). So that binary categorization is almost surely wrong.
Yet, we are heavily biased towards categorizing people and against seeing the full spectrum. Sometimes this bias is due to laziness, as labeling others as liars liberates us from the effort of actually understanding their claims. But less trivially, labeling others allows us to feel like part of a more exclusive group, a group that would presumably never commit such an error.
Surely, we must downshift our faith in the author's other claims some upon finding that they have made a mistake. But remember the high prior probability that the authors are merely fallible, and don't differ much in the degree of their truth-seeking from the rest of us. Now, if they get two things wrong...
Bottom Line: While it's healthy to be skeptical, it's healthier still, for the body if not the ego, to be appropriately skeptical of your own skepticism.