My general disagreements with those axioms from my reading of the literature are around the concepts of immutability and of the belief in the almost entirely biological factor, which I don't think is well supported by current research in genetics, but that may change in the future. I think primarily I disagree about the effect sizes and composition of factors with many who hold these beliefs.

I do agree with you in that I generally have an intuition that intelligence in humans is largely defined as a set of skills that often correlate, I think one of the main areas I differ in interpretation is in the interpretation of the strength of those correlations.