This is a great question. I can only really talk about one aspect, because it's the only area I know in enough depth to provide a decent answer. I'm going to focus on atomic theory (all things are made of atoms)

There's two ways to approach this. The simplest is to look at the history of atomic theory and see at what point it aligns with what is taught at highschool. So we could consider the discovery of the neutron in 1932 by Chadwick or the discovery of fission by Meitner as the turning point for atomic theory.

I think this is the wrong way to approach the question though. In order to be a leading expert it's not sufficient to simply propose a new idea; convincing other experts is much more important. This is the reason why Dalton is considered the father of atomic theory: he first produced convincing evidence for the existence of atoms, whereas the atomists of Greece were philosophically motivated.

Now we need to ask the question: what proof of atomic theory would an average highschooler be able to produce that would convince the experts of the day, using just the analytical techniques that existed at the time? This is a much harder question to answer, for two reasons. The first is that the history of science is usually glossed over, and so many students are simply unaware of how some of the widely accepted theories of today actually started. The second is the science learned at high school is highly simplistic, and often disguises the months or years of painstaking work that went into key experiments.

In order to actually answer the question, I'd disagree that a typical highschool graduate could ever convince the experts of the day of the validity of atomic theory. An exceptional student, who was aware of Einstein's work on Brownian motion, might have a bit more luck, particularly in the first half of the 19th century, but even then it would surprise me.

Or, given the number of things humans have believed throughout history that turned out to be wrong: how far back in history would a current high school graduate have to go to have a better understanding of various scientific fields than leading experts at the time?

Are we counting math? Newton and Leibniz both developed calculus in the mid 17th century. The majority of high school graduates don't know calculus, but some do.