Mr Nyhan suggests at the end of his paper that the best response to this problem may be "naming and shaming" public figures and media sources that spread mis- or disinformation. He points to the widespread discrediting of Ms McCaughey in 2009 as an example. I'm not sure how promising this is as a strategy. Organisations that begin with the aim of correcting false information, and devote themselves simply to criticising misrepresentations, tend with time to be seen by the public as tied to a partisan agenda of one sort or the other.
That's what has happened to Media Matters, for example; because it is dedicated to critiquing distortions by conservatives, its critiques carry no weight with conservatives. The way to maintain credibility as an arbiter of claims is to try to direct one's critiques fairly equally at both liberals and conservatives. But this can generate the same kind of false equivalency and he-said/she-said-ism that Mr Nyhan thinks contributes to the proliferation of public misperceptions of fact. It preserves incentives for each camp to try and skew the needles by pushing more outrageous ideological claims. I think Mr Nyhan is right that we need to invest some social capital in reinstilling a sense of responsibility in our political and media elite. But I'm not optimistic about any strategies for doing so.