The mistake which this podcast made was to misinform their listeners. Given that informing their listeners is their core mission, it's a pretty unforgivable mistake. Better to listen to another podcast which takes their mission more seriously.
Any podcast that has "informing their listeners" as a core mission will make mistakes now and then. It happens because we are all humans and not Gods. All I'm trying to do here is push back against the suggestion of the article that you write off people based on a single mistake. A world in which I can never make a mistake is not a world I want to live in.
There’s an obvious difference between a one-off mistake and one which is part of a pattern of continuous deception meant to bias the audience in one particular political direction; the mistake mentioned in the article is clearly the latter. It does not deserve the benefit of the doubt you’re giving it, as a genuine one-off would (particularly if they mentioned, corrected, and apologized for the mistake, which I predict with high confidence they will not do).