OK, let me spell out the first problem. (Calling MegMeg for the others!)
Consider a trait like height or intelligence that is at least partially heritable. For simplicity, suppose the adult value of the trait X is equally affected by genes G and environment E, so
X = G + E
where G and E are, again for simplicity, independent Gaussian random variables (normally distributed) with similar standard deviations (SDs).
OK, for simplicity let's allow him that, setting aside the total implausibility of genes and environment being independent.
Suppose that you meet someone with, say X = +4 SD (i.e., someone with an IQ of 160 or a (male) height of roughly 6 ft 9). What are the likely values of G and E? It's more likely that the +4 SD is obtained from two +2 SD draws from the G and E distributions than, say, a +3 SD and +1 SD draw.
In fact neither of those situations is even possible. Suppose G ~ N(mu_G, sigma^2) and E ~ N(mu_E, sigma^2) - he said similar SDs, we're giving the distributions identical SDs of sigma. Now given the independence assumption, X = G + E ~ N(mu_G+mu_E, 2sigma^2); that is, the SD of X is sqrt(2)sigma. So two +2SD draws from the G and E distributions correspond to an individual with x = g + e = mu_G + 2sigma + mu_E + 2sigma = (mu_G + mu_E) + 4sigma = (mu_G + mu_E) + 2sqrt(2)(sqrt(2)sigma). In words: in the X distribution, this person isn't a +4SD individual, it's a +2sqrt(2)SD individual.
Totally basic error. Not the only one, nor even the only one I can see. Not someone I'm going to trust on matters where I might not spot the basic errors!
