Let me answer quickly to one thing first, but I want to create a more complete answer with more analysis of the first couple of episodes later when I have time.
There are four different things. Let's say there is a novel with obvious fantasy elements. I'm fine with that. Let's call the fantasy elements "dragons" just to give an example.
The author wants to write a story about dragons, but they want to incorporate some elements of science. The author has the following choice (or a combination of the following choices):
1. Not incorporate any scientific elements.
2. Incorporate some fantasy science elements. The science of the dragon world is not the science of our world. (This is usually called magic of course.
)
3. Incorporate our world science in a way that is not correct. So it isn't real science the author incorporates, but just an appearance of science. Or what people (who are not interested in science and who have almost no knowledge of science at all) think science is. So it's not science that is incorporated but "perception of science". So e.g. a character can wear a lab coat and use test-tubes and fancy looking pipes etc. But no real science gets incorporated. This trick is often used e.g. in advertisement (fake doctors). This can be done on different levels. One level is just fully external perception (lab coats). One can go one level deeper and use real names of e.g. real chemical names. Like "nitric acid". One can go one more level deeper and use not only real names but some random facts to make the appearance of science more plausible. E.g.
Fact 1: "Saltpeter can be extracted from caves thanks to some chemical reactions happening with bat guano."
Fact 2: "Saltpeter can be converted to nitric acid by a chemical process which requires other substances as well."
Let's say these are scientific facts. The author can then do a leap from these two facts to "Nitric acid can be extracted from caves by using a bucket."
Of course we are still at point 3. No real science has been incorporated, because the sentence above is just not true.
4. Incorporate some real science. E.g. if I remember correctly, alchemists produced nitric acid in a reaction of saltpeter (I suppose it can be extracted from caves) with copper(II) sulfate, a form of which is present in chalcanthite. So the author can make the character go to a cave, get saltpeter and then go to another cave and get chalcanthite. Then the character can combine them, use high temperature etc. and get nitric acid. So things can be of course not said explicitly, but it assumes no things WHICH ARE SAID are wrong. In this way not only an "appearance of science" is incorporated, but some real science as well. It's not necessarily complete, some important steps might not be incorporated or explained etc., but no step which is incorporated and explained should be wrong.
So now it's time for my arbitrary value judgement of course. I think that doing 3 (with using all scientific terms and some scientific facts, not just lab coats and test tubes) but saying or pretending that one does 4 is misguiding the audience. I don't like to be misguided. And I don't think misguiding other people is a good™ thing. People who are less knowledgeable in science might e.g. truly believe that they can learn something valuable from it, maybe not complete knowledge, but at least that they won't be mislead by the author. They can truly believe that they can extract nitric acid by collecting water from a cave full of bat guano for example. Everyone knows that dragons do not exist, so it's obvious. The same with magic. It's also not a problem, if characters use lab coats etc. This is not misguiding in the context of a novel (but it might be in other contexts e.g. advertising). But what Dr Stone does is misguiding.
Of course not everyone might think that 3 pretending to be 4 is a bad thing. I suppose you and H03nn89 might be ok with that. And that's all fine. Nothing forces you to make the same value judgement that misguiding people in this way is a bad thing or you might also not think that people are actually misguided. The second option is testable. One can check by asking random people, if they believe that the "science" in Dr Stone is maybe not complete, but at least correct in principle and the author does not misguide them. If many people say yes, then they're misguided.
And the author and/or the advertisers of the novel are to blame. But if misguiding the audience is fine according to your value system, there is no problem for you at all.
