For me personally, situations like this make me trust science that much more. If someone finds that a previously published paper contained errors, as any human work is likely to, and the response is to go back and correct those errors or publicize whatever was wrong with the research, well that's science working as intended. That's freaking awesome.

What I get really, really, really frustrated with is the attitude that some people have where retractions of stories or articles makes them trust the source less, rather than more. If a journal publishes a retraction, I have that much more faith in that journal, and that much more faith in the scientific process in general.

Similarly: news outlets retracting stories or issuing corrections makes me trust those outlets that much more, because it shows that they care about making a best effort to present truth, and they care more about their reputation as being a source of facts than they do about whatever short-term backlash there might be.

Any media outlet, journal, web site, or other publication that doesn't regularly issue retractions and corrections is not to be trusted. It'd be better if the erroneous information didn't get out there in the first place, but there's no scenario where everybody gets everything right the first time, all the time- it's going to happen.

You can really see the different perspectives highlighted from people posting to social media in response to things like changing estimates of the age of the universe. There's always a contingent of outraged morons screaming stuff like, "now they're saying it's 5 billion years older than they thought it was before, and people continue to trust them?!? All those scientists are such hypocrites for doubting my belief in anti-vax/Austrian economics/chemtrails/Noah's Ark/etc., how dare they!" They act like changing your mind based on new data, or admitting you were wrong about something is a sign that you shouldn't trust someone, whereas I would say the ability to constantly revise your beliefs is a fundamental requirement for trusting someone's judgement. The inability to do so is a reason to not trust anything someone says.