To me, his most interesting assertions are the following:

• some kids are just smarter than others
• kids separate out into different levels of academic performance pretty early, like age 7-10, and then generally stay there into adulthood
• it's not possible for teachers or schools to "equalize" smart kids and less-smart kids, or privileged kids and unprivileged kids, but equality-minded liberals and leftists expect them to be able to do that
• the American public education system generally does okay given what's asked of it. Not great, but okay. A lot of the criticism it gets is undeserved.
• Allocating more money to schools probably would not lead to kids being any smarter or performing any better. Increased school funding only leads to better student performance up to a certain point, and the US is well past that point.
• the SATs and ACTs are fairly good assessments of who's smarter than whom, and of who is more likely to succeed in a four-year university
  • the criticism that they are biased in favor of affluent/white students is off the mark, or, at least, the alternatives to SATs/ACTs (like GPA and extracurriculars) are even more biased in that way
  • related to this, conventional IQ tests are fairly good at testing general intelligence, and left-leaning people are wrong to dismiss them
• the idea that there are huge disparities in school funding between white/rich areas and nonwhite/poor areas is incorrect. Yes, local school funding comes from property taxes and therefore will be variable between different localities, but state-level and federal-level school funding is redistributive enough that it overcomes that issue
• the achievement gap between white and black students (including the gap in standardized test scores) is not because of anything that's being done particularly wrong by our education system
• only 5-10% of variation in student performance is attributable to in-school factors; the other 90-95% is due to outside-of-school cultural/social/environmental factors, and/or is just endogenous to the students themselves
  • he sometimes makes an even stronger version of this claim, and asserts that even the environmental and cultural factors can be more or less set aside, and the real reason for differences in student performance is genes. But he's also backed away from that at times and said that "whether it's environment or genetics, my point still stands".
• there's no such thing as "good schools" or "bad schools", just schools with good students and schools with bad students
• the idea that American students are "falling behind" other countries is wrong. The reality is that American students kind of always were behind. US students have performed kind of mediocre in international comparisons with other rich countries for basically as long as these tests have been conducted; it's not a new problem. This was even the case in the 1950s-1970s, but it didn't stop the US from being the scientific & industrial leader of the world in that time. We still were curing polio, and landing on the moon, and leading the way in computers, and generally kicking ass.