Everyone should learn the most important ideas of human civilization. There should be a year-long lecture course that introduces all the "must see" ideas, the best that the human race has found, the stuff that would be tragic for a person to have lived and never learn. Certainly many things require lengthy study to be useful, and many things are already as clear as day to many people, but there are many important ideas of which educated people are ignorant.
Even if this makes sense for ideas, it certainly makes no sense for art. The survey courses in dance, art history, music history, and world literature probably can't be meaningfully condensed any further. But no one should miss out on the major ideas of the introductory courses in math, astronomy, physics, chemistry, biology, psychology, economics, computer science, philosophy, political science, philosophy, and history. Some ideas fall through the cracks of all of these intro courses. (For example, what about the central points of
The Death and Life of Great American Cities?) Some ideas are also too new to make it into conventional courses. For many ideas, only a few minutes explanation would be sufficient.
Many survey courses take the historical approach, but in this context it would waste too much time. To make it more interesting, the course (and more importantly the reading list) could touch on the limits of human knowledge and current work.
I originally had this idea in yeshiva, in a spirit of parochialism: "take this course, and then forget about the rest." Ironically, the course would probably not be popular with the insular (even if it were to omit evolution). This idea came back to me recently, thinking about John Rawls. I realized that neither my college survey in humanities nor intro to philosophy mentioned him.
The following are the ideas that I could come with quickly; please suggest more.
big bang, scale and elements of the universe, basic probability, limits, idea of calculus, newton's laws, four forces, electricity, nature of light, relativity, phases of matter, entropy, periodic table, cells, virii, bacteria, dna, systems of the body, evolution, milgram study, the unconscious, supply and demand, how a computer works and what a program looks like, urls, kant's categorical imperative, veil of ignorance, a myriad of -isms: utilitarianism, facism/socialism/capitalism(democracy), world religions, epistemology, problem of induction, logic and godel for dummies, mixed-use cities, human history in 30 minutes :), how toilets work