It undermines their credibility when they can't get a simple fact correct. If an article led with "the earth is flat", it may not relate to the article but it nevertheless makes me less likely to believe the rest.
b) The rest of us can accept the incentive structure that induces publications to write clickbaity titles like adults, rolling our eyes, and seeing judging the article on its merits. The publications aren't going to miss your attention anyways.