So far the science experiments of Senku and co. have been scientifically correct, as the materials and elements are nonfictional (unless there was something there that was and I didn't know about it).
Has there been something people have barely missed in the current anime episodes and manga till the current chapter that is surprisingly fictional?
The whole "petrification beam that turns people into stone, keeps them on suspended animation for several thousand years, and heals all injuries" concept that the story is based around is clearly fictional. We don't know how to replicate most of that with even theoretical science.
The A.I. on the International Space Station is more advanced than anything we can make right now.
Also, the recent manga chapters indicate that apparently
there is someone living on the moon that is behind the original stone beam, and they may or may not be nonhuman (i.e., aliens). Sapient aliens aren't impossible, but we don't know of any right now.
Preamble: proving the absence of something is a daunting task.
In this case, it would require having seen every episode and read every chapter with the utmost attention to every detail, and being able to answer every possible "Is THIS based on real-world science?" question.
Pointing at a specific event and asking whether (or to what degree) it conforms to actual scientific facts would be far more feasible a mission.
Having said that, and having added that I haven't read the manga, I think the anime makes a point of being scientifically accurate, so much so that every episode end with this statement:
This is a work of fiction, but the plants, animals, and production methods described are based on reality.
Foraging and making things on your own accord is extermely dangerous and, in some cases, illegal. Please do not imitate without expertise.
Proving the power of scientific knowledge (especially in a world that has forgotten it) is the main theme of the show, and having the characters succeed because of fictional elements would clearly undermine it.
If we want to find shortcomings, I think we can find them not in the presence of imaginary elements but rather in the handwaving of some "logistical difficulties".
For example, the fact that the "Kingdom of Science" is withing walking distance of gold, copper and iron ore deposits (to say nothing of the other minerals) and a pool of sulfuric acid is extremely convenient plot-wise, but probably a bit unrealistic.
