Can democracies function properly without a broad bare modicum of scientific understanding? What can or should we do to make such muddled thinking firmly a thing of the past ?
I would say that modern societies can function without a broad scientific understanding of many people (actually they do it right now quite well), as long as there is a sufficiently large (or "critical") number of people who do have that understanding and the ability to influence at least the decision making part of society. An simple example would be: you don't have to know exactly how you microwave oven works in order to use it (but the guy who built it should have had that knowledge).
A second problem is that the modern world has become so complex that a single human cannot accumulate enough knowledge in just one lifetime.
But looking at history I am very afraid that we cannot do anything to avoid such situations as described by Chris Ransford - people have always and unfortunately will allways prefer easy answers (or even worse: no answers) to more complicated, but correct, ones. Therefore you would somehow have to "force" people somehow at least to learn at one point of their life about such things (which is the basic concept of traditional school systems). But even this did not remove the thinking barriers or the prejudices against scientific method entirely.
So I guess (rather pessimistic) that the only thing we can hope for is to reduce, so to speak, the level of ignorance in society...
Learning from history I think some rock bottom understanding of the basics is absolutely requisite, I find the CNN's anchor comments frightening. Remember how the Aztecs used to perform wide-scale human sacrifice to placate the sun, lest it would refuse to rise in the morning ? Historically, arrant scientific ignorance has been a big-scale killer
but this is allready done (to a quite big extend): there are a lot of magazines like "Scientific American" or "Spektrum der Wissenschaft" here in Austria or Germany and in other parts of the world where scientists write articles about their fields in a way that can be understood by the majority of people. There is also a vast amount of popular science books (like "The elegant universe" by B. Greene or the books by Steven Hawking). So there is to my opinion no really "excuse" like "the scientists have to do more to bring their knowledge to the people. Everyone who cares can go into a bookshop or the internet and have access to this type of knowledge. This was never as easy as it is today...
Furthermore you can only have simplification for the price of accurateness, but the fact is that with deeper understanding of scientific questions also the answers become more complicated. Hence sooner or later you will reach a point where you can only work with analogies or you have to have a publicum with a certain base of knowledge in order to understand what you are talking about.
Interested people will be also willing to spend their time and brain cells to follow a certain field of interest - but these people would have done that anyway (so they need not much encouragement in the first place). On the other hand people who are not interested at all won't become interested just because there is more "data" available. Hence the necessity of a "forced" compulsory education (which in the end only serves the society because it creates a sufficient amount of skilled people).
@Chris: no, it's not requisite because the Aztecs (for example) had a very advanced civilisation (so had the Greeks or the Romans and they had a quite brutal way of life) - for the sun: they didn't know better at that time (I guess even their "wise men" had no deeper understanding of that).
But of course you are right with your other points: it is very frightening that a CNN reporter asks such stupid questions in a time and society were he could and should know better and also that ignorance ist often followed by violence
But such information can be found in every bigger newspaper (at least here in Austria) both in the print and in the online version with the possibility to get tweets about these news or something like that.
Here is for example such a Austrian daily newspaper with a quite big science section:
http://derstandard.at/Wissenschaft
(it's unfortunately only in german, I think, but it covers lots of new discoveries in all fields from history to astrophysics)
People can also discuss these science news in the integrated internet forums (but most of the discussion is just rubbish or studpid statements - mostly about politicians and the climate change, regardless the topic of the article).
However I like your idea of a newsfeed with important, simplified paper titles, but I doubt that this will help reaching the people who aren't interested in science at all.
But I truly hope to be wrong with my opinions, because it's much better to be an optimist than a pessimist who is always right ;)