Uh, quite simply, until you figure out how to fund education at millions of dollars per student (K-12), some ain’t! You’re asking for utopia here. Every teacher will never have a doctorate to teach a subject (even in college they don’t). At some point, if they’re lucky, most kids will develop some critical thinking skills. If not, such is life.
Few will grow up to become scientists. The entire discussion is lost on a very large percentage of the remainder (and too many who do go that route, that's why we're having this discussion). The idea that whether or not “some” people might come away from a television show with a poor grasp of the science involved should affect whether it be shown or not, would imply no fiction or “edutainment” should be shown.
We must save them from themselves! They can only watch stuff containing long litanies of what everybody (besides the author, director, producer) feels should be included as catchalls.
Take “Shakespeare in Love” (to avoid limiting the discussion to science only, education is bigger than just science). How long a list of historians should be granted time in the movie, to point out the lopsided view of historical health/care it provided, or dieticians on meals, socialists on politics, and actors’ union reps to highlight the inequities of men only casts, et cetera, et cetera. All because, if they aren’t granted equal time, the audience may come away with a “slanted” perspective!
If it will make you happy, have every high school graduate sign a disclosure statement at graduation to the effect that they understand that much presented to them as “scientific fact” is NOT. (Most’ll still flee screaming from second hand smoke and remain convinced global warming will kill the planet in 50 years.)