This is an interesting theory, and I am surprised that it hasn’t been discussed more on the forums here. Let me see if I can toss something into the mix. For those of you wanting some good reading Elaine Morgan’s books are well written and interesting, whether you buy into the whole aquatic ape theory or not. This stems from the web, books, and my own thoughts.
The first thing you need to remember about evolution is the time frame. We are talking about VAST amounts of time, geologic in scale, even when speaking of punctuated equilibrium. A lot can change in that amount of time. All of these adaptations probably did not occur at once but rather in a series, each one allowing greater access to food sources and the ability to escape predators by exploiting both land and sea. Also remember that in Darwinian terms traits don’t always have to be of primary value, but can be secondary, tertiary, or even quaternary to other, more beneficial traits. It is also important to remember that traits don’t evolve into the most efficient structures necessarily, but rather just efficient enough to get by. Only with further selective pressure does the next round of adaptations move through a population.
Hair – I have a feeling that lack of body hair is a byproduct of living in a warm, moist environment. Assuming that early man spent a lot of time scavenging along the seashore, in and out of the water many, many times a day having a layer of dead, moist, bacterially active protein next to your skin is a bad thing. Think of the critters, fungus, and germs that would breed in there. With the selective pressure of cold being absent it would be easier to lose most of the hair rather than adapt it to water. It stayed thick in the armpits, groin, and head most likely because that is where large amounts of blood (veins, arteries) pass close to the surface and you lose a lot of body heat. Probably important if you are in the air any amount of time. The rest of the hair could definitely go. Is it critical? No. Would it make the population a little bit healthier? Perhaps enough to be selected for, especially if coupled with another more primary trait.
Breathe Control – This one is a pretty strong argument. No other simians that I know of have it. It is why we can talk. The only reason to have it is to dive under water. It isn’t necessary for communication; lots of other animals don’t need to stop breathing to vocalize. If anyone can think of any other reason you need to be able to hold your breathe other than diving I would love to hear it.
The other human peculiarity is called "the descended larynx". A land mammal is normally obliged to breathe through its nose most of the time, because its windpipe passes up through the back of the throat and the top end of it (the larynx) is situated in the back of its nasal passages. A dog, for example, has to make a special effort to bring its larynx down into its throat in order to bark or to pant; when it relaxes, the larynx goes back up again. Even our own babies are born like that.
A few months after birth the human larynx descends into the throat, right down below the back of the tongue. Darwin found that very puzzling because it means that the opening to the lungs lies side by side with the opening to the stomach. That is why in our species food and drink may sometimes go "down the wrong way". If we had not evolved an elaborate swallowing mechanism it would happen every time. This arrangement means that we can breathe through our mouths as easily as through our noses. It is probable that this is an aquatic adaptation, because a swimmer needing to gulp air quickly can inhale more of it through the mouth than through the nostrils. And we do know that the only birds which are obligatory mouth breathers are diving birds like penguins, pelicans and gannets. As for mammals, the only ones with a descended larynx, apart from ourselves, are aquatic ones - the sea lion and the dugong.
Sweat- We sweat out of the wrong glands. We use enormous amounts of water and salt when we sweat. We are the only mammals to do so. So, one can interpret this to mean that humans evolved in a place that had large amounts of potable water and copious amounts of salt (unlikely to find either on a savanna). In fact, salt is one of the most difficult trace minerals for animals to find. Deer and elk, for example, seek out any source of salt. This is why salt licks are effective. One of the few places salt is readily obtained is near the sea. Something to think about.
Humans have 2 distinct types of sweat glands. One type is the eccrine, or sudoriferous, glands, which serve a cooling function. The sweat secretions which pass through the lumen of eccrine glands are never accompanied by cell secretions. Thus, scent-producing substances which are byproducts of cell metabolism are not secreted by these glands. They do, however, cool extremely effectively when combined with naked skin. Hominids are particularly sensitive to heat because of their large brains but lack of carotid rete. This defends against counter-arguments - savannah animals have not lost their fur and that shaving a sheep causes it to overheat in the sunshine. - the second point answered by bipedalism. Full benefit of nakedness only comes with sweat glands and bipedal posture. You have to be mostly upright to get the best exposure for cooling. This also might explain the hair tract orientation too. Further, thermoregulation hypothesis of bipedalism is self-defeating. It relies on grassland, specifically. No trees to block the breeze at shoulder height but some grass to block the breeze at knee height - otherwise why go bipedal. The sweat cooling must be fuelled by water but next to water you find trees. Plus what were they doing, wandering around in the mid-day sun? Looking to pick carrots?
The second type of sweat gland found in humans, called apocrine glands, are responsible for the production of body odor. Portions of secretory cells found near these glands enter the gland’s lumen along with the sweat secretions. These cells secrete a substance which contains fats and proteins. When apocrine sweat, combined with cell secretions, reaches the skin’s surface, the normal flora of the skin act on the sweat to produce body odor. While eccrine glands are distributed more or less uniformly across the skin, the densest collections of apocrine glands in the human body occur in the axillary organs (armpits). Clusters of apocrine glands are also found in the suprapubic region, circumanal region, perineum, face, scalp, and umbilical region of the abdomen. These secretions are unique in humans. In particular, septum secreted in mass amounts on the upper back and face may break down in such a way to actively retain moisture in the skin and protect from sun exposure, especially with the repeated drying effects of water and sun exposure. It is common knowledge that people with oily skin and acne get less symptomatic when exposed to sun and water – the two factors tend to clean the skin of the huge proteins that are being secreted in large amounts. Instead of “drying out” they “clear up”. This is conjecture, but probably as accurate as anything else.
Fat - Humans are by far the fattest primates; we have ten times as many fat cells in our bodies as would be expected in an animal of our size.
There are two kinds of animals which tend to acquire large deposits of fat - hibernating ones and aquatic ones. In hibernating mammals the fat is seasonal; in most aquatic ones, as in humans it is present all the year round. Also, in land mammals fat tends to be stored internally, especially around the kidneys and intestines; in aquatic mammals and in humans a higher proportion is deposited under the skin.
It is unlikely that early man would have evolved this feature after moving to the plains and becoming a hunter, because it would have slowed him down. No land-based predator can afford to get fat. Our tendency to put on fat is likelier to be an inheritance from an earlier aquatic phase of our evolution. It is true that some apes, especially in captivity, may put on weight, but we still differ from them in two important ways. One is that they are never born fat. All infant primates except our own are slender; their lives may depend on their ability to cling to their mothers and support their whole weight with their fingers. Our own babies accumulate fat even before birth and continue to grow fatter for several months afterwards. Some of this fat is white fat, and that is extremely rare in new-born mammals. White fat is not much good for supplying instant heat and energy. It is good for insulation in water, and for giving buoyancy.
The other difference is that in our case the subcutaneous fat is bonded to the skin. When an anatomist skins a cat or rabbit or chimpanzee, any superficial fat deposits remain attached to the underlying tissues. In the case of humans, the fat comes away with the skin, just as it does in aquatic species like dolphins, seals, hippos and manatees.
Eyes – As Eric noted- myopia is prevalent and is useful in the water. While I am sure it is exacerbated by reading/pc use the fact that we are so predisposed should be an indicator of something.
Diving Reflex – I don’t think any freediver can doubt its veracity, and similar reflexes (vasoconstriction, blood shift) has been noted many times in other aquatic mammals.
Hope you found this long-winded but informative,