The traditional answer to the first question is more or less "everything". Much like nutritionists advise a varied diet, educationists advise learning a wide variety of subjects. It is true that higher education has tended to focus on narrowed learning, where the student has a better chance of being an expert and of knowing more than the average person. Men, by the way, often want to "win". They don't much care at what, just as long as they win. So, there is a tendency for me to become the world expert in the use and history of the comma or the history of the letter A.
The 1939 education classic "The Saber Tooth Curriculum" tells the fictional story about the requirements to learn the moves and strategies of saber-tooth tiger hunting, despite the fact that such beasts are extinct. We have expert hunters or experts in what are believed to be advanced saber tooth tiger hunting and we require our youth to pass exams in the knowledge and skills of such hunting. Why? Who cares? I had to learn it and they are damned well going to learn it, too!
Which brings us to the other hard part. You teach 100 youngsters tiger hunting or Latin or the history of the ether. They look like they paid attention. They all were present for every lecture, every discussion. But the public and the parents would like more convincing data.
We have the demonstrations and the history lectures on tape and we can show 100 or 1000 students the tapes at a time. Not an expensive proposition. But the testing, the verification - that gets a little more costly. How about a multiple choice test, where we can arrange seating far enough apart that copying is nearly impossible? We feed the tests through a machine that reads them and tallies up the number of "correct" choices. There will be a few geniuses who can see a problem with all the choices to many of the questions but only a few. There will be a few students with extra high levels of worry and fear. We can test those who seem extra worried for blood pressure and such and give them a more personal test, maybe with an extra fee required. It is expensive to build the test and we will be afraid that some enterprising group will each memorize one or two of the questions according to a pre-arranged plan and reconstruct the test for sale to next year's students.
The most basic difficulty still remains. That is determining whether knowledge and skills of saber-tooth tiger hunting makes a large enough positive contribution to the later lives of the students and their society. Don't forget that those who want to focus on the joys of music are urging educators to drop saber tooth tiger hunting and emphasize flute instead.
I am not sure we will ever get this right. The problem is like a paraphrase of Ecclesiastes 12:12 "Of the making of educational adjustments, there is no end."