The book, originally written in 1981, describes Gould's objections to:
In the first edition, published in 1981, Gould made a number of critical points concerning many of the studies Herrnstein and Murray were to draw on. Gould's larger point is that most scientific studies of the relationship between race and human behavior have been heavily biased by the assumption that human behavior is best explained by heredity. He criticizes studies of the relationship between race and intelligence on several grounds. One thing he points out is that much of the data used by scientists was falsified (for example, in the case of a famous study of the IQs of twins separated at birth). But most of his criticisms pertain to cases where the data seems to be legitimate. Most of his arguments have to do with the value of statistical correlations (the measure of the co-occurrence of two different things). Most arguments around IQ center on the issue of correlation -- the very claim that the test measures an actual thing requires that the kinds of answers to various questions will correlate highly; the claim that this thing is inherited requires that the scores of respondents who are closely related will correlate significantly higher than results of those distantly related.
First, he points out that correlation is not the same as cause. As he puts it, measures of the changes, over time, in "my age, the population of Mexico, the price of Swiss cheese, my pet turtle's weight, and the average distance between galaxies" will have a high positive correlation -- but that does not mean that Steven Jay Gould's age goes up "because" the population of Mexico goes up. Second, and more specifically, a high positive correlation between parents' IQ and children's IQ can be taken as evidence that IQ is inherited -- or that IQ is determined by social and environmental factors. Since the same data can be used to argue either side of the case, the data in and of itself is not useful.
Furthermore, Gould makes the subtle and often ignored point that even if it were demonstrated that the correlations in IQ within a group were completely determined by heredity, this tells you nothing about the causes in differences in IQ between unrelated groups or whether those differences can be changed by environment. One example that Gould brings up is height which is known to be highly inherited. Knowing that differences in height within a single group are due to heredity tells you nothing at all about why there are height differences between different groups.
In an interview in The Skeptic, Murray claimed that Gould misrepresented his views. Arthur Jensen made a similar complaint: