There are many problems with our secondary and primary education systems.
In general, I would say the problem is many-tiered. On the top, you have the government, which is parly to blame for bureaucratic incompetence. Under that level the problem separates into several distinct branches: Parents/teachers, unions, students, money, municipal overburden, culture etc.
For starters, the problem begins in the culture and and home. American culture centres around an distincty anti-intellectual "anti-elite" mentality. They have a phobia of any experts or "elite" educated officials. Instead, they focus on the worship of the "common man," which is a sad hold-over from the age of Jackson.
More specfically, intellectualism is frowned upon by the masses, which influences parents and children. Poor education starts at the home. There are many good parents, but there are also many poor parents; good parenting is not innate. Many parents don't have time to help their children or they don't want to because they are "busy" with something else. Other parents simply don't care or they are unable to help because of the technology and educational gaps between generations. Religion of the parents can also be a hindrance.
Speaking of which, communities having too much say in what is taught is also a problem. Education is needs to take tips from the superior nations and focus more on allowing the experts in the fields create and administer curriculae instead of communities and bureaucrats who know little. (IE. KANSAS and DOVER affairs). We need a better, more relavent curriculum focused on the sciences, languages, logic, math, grammar, civics, ethics etc.
As for the schools, the curriculum itself is poor in many areas. THey are focusing on the wrong subjects and they are teaching them incorrectly. The pedagogy is not one that encourages critical thinking or logical analysis; they simply don't teach it. Instead, they teach rote memorization. To compound this problem, people are more fixated on making the kid feel good emotionally than actually teaching him. You should do both, but not do away with the latter in favour of the former.
Another problem is we have poor discipline at home and at schools, and people aren't allowed to deal with this. We tolerate bad children and problem causers in the classrooms and give them far too much leeway. Half the punishments are retarded as well.
There are also too many days off, not enough days in school learning. Singapore, Japan, and many other asian nations have superior public education. We are obviously doing something wrong.
Unions are also part of the problem in that they wield far too much power to the detriment of the children.