Here's what I'd (try to) do/change:
Teacher's Unions reform.
laws involving better pay and minimal requirements, in particular for HISTORY teachers. Too often, it's the Coach who teaches you the really, really relevant death of Crispus Attucks. You should spend as much time on World History as you do on US history.
I think that if philosophy were done right at a high school level, it would provide an excellent alternative to the English courses that teenagers love to hate. It might have a greater social benefit in the long term, as well (critical thinking, advancing adolescent thought beyond nihilism).
United States citizens suck at geography. On an unmarked political map of the world, you should, at some point, be tested on the following:
North America: know which one is Canada, which one is the US, and which one is Mexico (know your ass from a hole in the ground). Seriously. People on Jaywalking....
Europe: Identify each country by its borders, give its capital, and tell me a little something about it. (I admit I would have to study for Eastern Europe, but that's the fun thing about bitching about education when you're an adult-you don't have to put up with the crap yourself).
Australia, Antarctica & Russia: know your ass from a hole in the ground: i.e. identify them. Be able to tell me a little bit about them (the fact that there are science claims on certain bits of Antarctica, etc)
South America: know each country, which one/s speak Portuguese as opposed to Spanish.
Africa: Bix Nood. Just be able to tell me which one South Africa is (lol Public School), which one's Egypt, and where the Sahara is (all them North African countries)
And then there's tech. How shall we compete with Europe and Japan? I think
>>8 is absolutely right. I'm not too worried about the triumvirate of physics, chem and calc. They're there for the kids who want them, but the problem is to get HS level teachers into those areas.
Another thing which no one has touched on is the fact that public schools have been made to shoulder exponentially more parental responsibilities over the years. TAKE the money from those programs, INVEST in BETTER TEACHERS, and you'll have money left over for precious football. It really is all about the teachers. That's my sweeping generalization of the day.
Lastly, licensure and legal matters are so stringent nowadays. The person who knows their shit should be the one to teach.