You're shown that getting results is straightforward: get rid of poor teachers and reward good ones. One stat that was particularly interesting, from a Stanford researcher whose name I forget, was that replacing the worst 6-10% of teachers would put us on the same proficiency level as Finland.
Unfortunately, the system makes that very difficult. Many teachers are granted tenure, making them impossible to fire, and educators' compensation isn't designed to allow for performance incentives. Contracts demanded by unions are partially to blame.
Also, our education system was built for previous generations' economies. Professionals, scientists, technical workers, factory workers, and laborers were needed in different proportions than they are today. Now we have more highly skilled jobs without enough highly educated Americans to fill them. SV and schools in Redwood City and Woodside are mentioned specifically.
It examines the costs of poor education, like the staggering number of dropouts who end up in prison. Their incarceration cost could put them through private school with money left over for college.
Saying the film demonizes Weingarten is exaggerating. She doesn't look great, but there are clearly a lot of factors at work.
Waiting for Superman makes clear that the way forward is good teachers.