Maybe this question will be more pertinent. Science has supposedly calculated the number of mutations necessary to go back from man to the nearest simian ancestor. How can that number of mutations be broken down into individual changes, such as the restructured pelvis, vocal cords, feet instead of grasping paws, lack of fur, intelligence, self-awareness, language, etc? I think they would fall far short of the number necessary only through haphazard changes to DNA.
First off, "simian" can refer to apes or monkeys, so I don't know what ancestor you are trying to refer to. As far as mutations being broken down into individual changes in physiology, remember that it is entire populations that evolve, not individuals. However, I'll try to answer your question to the best of my ability regardless.
So, to begin with, you have fundamentally misunderstood what "science has supposedly calculated". It's an approximation of a likely evolutionary path. We can't quantify the number of mutations between us and, say, Homo habilis, because we don't have access to Homo habilis DNA and thus we can't determine how genetically distant that species is from our own. In fact, any claim that the fossil species we discover are definitively ancestral to us is flat out wrong. Without DNA, we'd never be able to know that for sure.
What we can do is distinguish the physical traits and genes we do and don't share with other modern ape species besides ourselves, and give approximations as to how long ago our evolutionary paths split. Remember, chimpanzees are our evolutionary cousins; we didn't evolve from chimpanzees. Basically, the traits we do share existed prior to the evolutionary split, such as the fact that humans and chimps have the same blood types. The ones we don't came after. Since we know the average mutation rates in apes, and we know the modern similarities and differences, we can roughly calculated how long ago the split was mathematically. That is, we start out knowing how many sequences in our DNA are shared between us and our closest modern relatives (bonobos and chimpanzees) and work backwards to find the time. So, the difference between human and chimp DNA is about 1.2%. For simplicity sake, I am going to use the number of base pairs in human DNA for calculations (3 billion) and the low end for the average number of mutations per person that is born (40). Multiplying 3 billion by 0.012 (1.2%) makes for approximately 36,000,000 differences in the base pairs. Divide that by 40, and I get 900,000 individuals as the minimum to be born for humans and chimps to diverge (obviously, more individuals were born than that and this isn't all in one generation). So, let me be very cynical, and say that each of those individuals represents an entire generation, and that each generation is 15 years apart. My result is that human and chimpanzee evolution diverged about 13.5 million years ago.Now I'll use Google to check the actual estimate for that... 12.1 million years ago. Not too bad, considering that I purposely used worst case scenarios.
As for self-awareness, uh, humans and chimps share that trait. In fact, all apes are self-aware, as well as dolphins, many birds, and elephants, to name a few. And even bees and ants have language. How we utilize these aspects is a matter of our intelligence. What makes our minds so advanced compared to a chimpanzee? Not much, it's mostly a matter of size, since chimps share most of the same brain structures as us. You can attribute most of that difference to the fact that there are 2 groups of genes which serve functions in other apes, but have mutations in humans that leave them non-functional. 1 group of genes functions for the generation of a muscle that attaches to the skull and jaw (and has the secondary effect of restricting the expansion of the skull and brain case, limiting the size it can achieve). The other group of genes are regulatory genes for brain cell division and growth. And that's about it. Some broken genes made our jaws weaker but gave our skulls more room to grow, and other broken genes caused our brain tissue to grow and divide at ridiculous rates; almost cancerous rates, which is why we are so much more prone to brain cancers than other apes.
Addressing the other traits you mentioned, they vary from just a few mutations to dozens, and mutations often impact more than one part of the body, so there is overlap. Furthermore, while mutations are mostly random, natural selection is not. Individuals with traits that help them survive and reproduce will pass those traits down to the next generation, and those that have traits that kill them or significantly reduce reproductive success will not contribute so much to the next generation. Intelligence is such a beneficial trait to survival that our increased cancer risk and weak jaws don't outweigh it. Walking upright and having the hands freed up to manipulate objects is such a beneficial trait that the fact that this method of locomotion wears our bodies down and inflicts us with back pain and spinal problems doesn't outweigh it.