it's well understood at this point that the genetic contributions to intelligence are minimal to non-existent, and the exception more than the rule. intelligence does not exist entirely independently from genetics, but it is shaped dominantly by the environment.
but, that's kind of actually the point that's really being made, here - the film isn't arguing for the genetic basis of stupidity, so much as it's arguing for the environmental effects on it. it may be the case that there is no particular genetic reason why two very stupid people could not produce intelligent offspring, but because the factors in intelligence are so intertwined with environment, it does stand to reason that people that are raised by stupid people are going to end up just as stupid as their parents.
rather than cite very old and debunked studies and present them as a strawman argument around the intent of the film's creators, i'd rather direct you to studies regarding public v private schools. up until recently, private school advocates would point to higher grades as evidence of superior schooling, and it even led to support for voucher programs. but, over time, greater study led to the conclusion that the differences in grades had to do with class and upbringing rather than instruction.
that is to say that the modern science is actually pretty clear that how you raise your child is a dominant factor in how intelligent they end up.
he'd have realized that if he wasn't.....an idiot.
regarding the pseudo v anti intellectual section, i'm just going to say no and leave it at that. pseudo-intellectualism is a thing, surely. but, we live in anti-intellectualism more than pseudo-intellectualism, and i'll point to your decision to present the argument without any sort of backing as evidence of that. i realize i'm doing the same thing, but i don't have the burden of proof, here, and i don't know of any studies that analyze the question and attempt to come to a meaningful deduction.
there's a lot of criticism of the film out there and...
it's all very ironic. truly.