Wow. This thread has drifted way off topic with all the discussion about dietary science. It’s all very interesting (especially since I’ve been on a drive over the past 18 months to lose weight myself), but it should perhaps be spun off into a separate discussion.
Coming back to the original question of how much science we should expect non-scientists to understand, it seems that people have been making quite a persuasive argument for “None whatsoever.” The fact of the matter is that compulsory school level science education in some countries is pretty pathetic. You get taught a whole lot of facts and end results, but it can all seem pretty disjointed at times and it’s only once you start to specialise that you are taught the underlying principles of what ties it all together and how scientists know what they know. On top of that, many kids don’t pay any attention in science class either. I remember one biology class when I was fourteen, we were doing an experiment with earthworms and two boys started playing a game of table tennis with the worm as the ball and their rulers as bats. Needless to say that was not one of the objectives of the experiment.
Having said that, I don’t think we should set the bar so low that they get away with everything. At the very least, they should be able to understand, when it is pointed out to them, that there is such a thing as measurement, that it is constrained by strict rules, and that the rules apply to every context. Even if they struggle to get a grasp of what the rules actually are.