The problem, in my experience, is that most people are happy to learn "how to apply critical thinking to judge news stories," will agree to the principals in a general sense, and then go on and only apply such tools towards things they are biased against and while uncritically believing any reporting that either confirms their bias or seems to be part of the common sense of their peer group.
For instance, NPR talks about news literacy here, and I'm sure most of the people at NPR "know" how to be critical, but their level of reporting often doesn't reflect that.
For another example, there's a podcast I listen to by journalists that often point out poor reporting and misinformation spread by other journalists. But they'll usually uncritically repeat the "common sense/everyone knows" ideas that permeate the media outside of their wheelhouse. I only saw a realization of this issue once, when they were talking about the Gell-Mann Amnesia affect, then a couple of minutes later were talking about news reports showing XYZ, and they gave some throw away disclaimer to the effect of "although, I suppose going by the Gell-Mann Amnesia idea, we perhaps shouldn't trust these reports 100%."
In the end, it seems that news for most people serves as a form of infotainment. Infotainment that spreads a lot of disinformation, but leaves people with the illusion they're informed. I think most people would do well to take a few months off from the news and see how it effects the things they actually have control over (usually a lot less than they assume), or how out of place they'll feel when they jump back in (usually not much, since it seems most news items are forgotten within a few weeks).