This anatomic conception of merfolk (mermen and mermaids) is an amalgam of biological particularities found in in sea mammals (dolphins, whales, manatees, sea lions) and sharks. Some are not found on Earth, but are still plausible. My idea is separated in four part for simplicity.
First, the metabolism, body strength and internal anatomy:
The vascular system would be made in such a way that the body could stay warm without the need of an overly thick layer of blubber (marine mammal fat).
The inside of the lungs would have two layers of oxygen-carrying capillaries and twice the number of alveoli found in those of humans, permitting long diving sessions of fifteen to twenty minutes.
The muscles of the body provide a specimen with a strength ten times greater than the best human athletes; however, because of the body shape of a merfolk, it would be inhibited on a land mass (shore, rock on which they get heat from the sun and seduce sailors).
While in water, if a merfolk cannot have access to air on the surface, they can slow their metabolism to rely solely on their hair for oxygen (explained in part 2).
The throat has a larynx able to emit sounds in the same frequencies that can be heard (explained part 3).
Salt glands expell the excess of salt in the body via the anus, keeping the orifice clean in the process.
The blubber contains organohalogens which prevent the body getting infections in case of gaping wounds and acts as a buoyancy agent. The cellular regeneration and immune system is so efficient that even open wounds takes just weeks to heal.
Second, outside body features:
The teeth would look like ours, but be sharper because their diet is comprised of bones and shells. A tooth is able to regrow when lost.
The hair (and beard for the males) would be very long, able to absorb oxygen like gills and detect pressure changes due to movement. The color could be dark blond, black, white, grey. It would gain a tint or become completely green over time because of the presence of algae. It could become a small ecosystem which both attract prey and serve of camouflage for the mermaid.
The hands have retractable webbing and hard nails that can be used as claws if sharpened and not pedicured.
The iris colors could be either silver, amber, emerald green, dark orange, light and dark brown, nearly black, or dark or light blue. The pupils of the eye would glow red or silver if exposed to light in dark water because of the presence of a tapedum lucidum in the back of the eyes.
The tail, based on the lower part of the dolphin, would have caudal fins for reproduction purpose. A urogenital slit placed over a anus would be located between the caudal fins.
Nasal membranes placed deep in the nostrils can close at will, stopping water from reaching the lungs while letting smells in.
Third, the senses:
The sense of hearing is seven times more developed than human because the head possess three time more ear cells, making them able to perceive frequency from 20 hertz to 150 kilohertz.
The sense of smell has a range of hundreds of meters.
The sense of touch is very developed, making a individual more skin-sensitive than a human.
The range of taste is limited to the basic (salty, sour, sweet and bitter) but the taste buds detect potential food over many kilometers in water.
While the eyesight is in the same range as humans, the perception of their surroundings is superior. They are capable of echolocation like dolphins, which provides them with a bio-sonar, and electroperception like sharks, because of the receptive organs called ampullae of Lorenzini.
Fourth, the drawbacks:
Because of the body shape of merfolk, their strength is near useless on a land mass (shore, rock on which they get heat from the sun and seduce sailors).
Because of the particularity of the vascular system, bleeding would take longer to stop, forcing the wounded merfolk to go on the surface to speed up coagulation.
Things I learned after this post :
Great concentration of myoglobin in the muscles would extend diving time because it is good at retaining oxygen.
The hair cannot be used to supply the body in oxygen. Their length could lead to entanglement, letting them to be cut, and development of algeas on the filament would block the absorption of oxygen. It would let body heat escape, while body heat is crucial to keep in a marine environnement.
The urogenital slit and anus would placed just below the waist, not between the caudal fins.
They either use echolocation or electroreception, not both of them. If it is echolocation, it would be the shorter range kind.
They could consume some crustacean with their carapace, but for the mollusk it would be only the flesh and not the shell.
Too much muscle mass would compromise floatability. Only if the lower part of the body that has a strength ten times greater than the best athletes and the upper portion has the strength of a normal human torso(albeit very fit because of near constant physical activity), it would keep a reasonable amount of floating capacity.
No need for salt glands, the body of marine mammals can balance it salt concentration by the use of very efficient kidneys and super-concentrated urine.