The hospital on Unst when first seen is named "Saxa Vord Private Hospital", the second time it is called "Mount Carmel Private Hospital".
When Tora confirms Dana's pregnancy, she says Dana is only six weeks along. But by the end of the movie, Dana has not only carried the baby to full term, but has also given birth, with no hint of any kind of timeskip taking place.
Male contraceptives drugs render the males infertile or inhibit ejaculation or poison sperm motility. They do not cause miscarriages in pregnant women.
The medical examiner in the film claims that the peat secretes an enzyme that disturbs the bacteria. This is misleading. The anaerobic conditions of the bog and the pH of the peat are what preserve the body. In a sense, it's much like pickling. No bacteria consume the corpse because there is no air for the bacteria to grow. Given that, the flooding that the film states occurred in 2012 before the events of the film could not have disturbed a body entombed 6 feet deep in a peat deposit, as there's no "enzymes" to dilute and the preservation of the corpse occurs through other means inaccurately left out of the film.
When Tora steals the boat and lands on the island, she leaves it far up on shore several feet from the water. If it had been a small boat, she possibly could have dragged it there, but it was much larger-- the size of a ski boat or patrol boat, much too large for one woman to drag across dry ground.
It would have been easy for the medical examiner to notice the corpse discovered in the peat was that of a nursing mother. Peat bogs preserve fats, in fact ancient cultures would preserve butter by placing it in a animal bladder and sinking it in a bog. This would preserve the fats of the butter indefinitely. "Bog butter" preserved in the ancient past is still edible today. A nursing mother would have had deposits of bog butter and a substance called "grave wax" in the tissues of her breasts, and most likely in her hips and thighs as nursing mothers tend to accumulate fat reserves more so than other women. Easily noticeable in even the most cursory medical inquest.
When the crime scene investigator is examining the remains uncovered in the horse paddock, he says that her body is tanned from the peat but her bone structure indicates she's Caucasian. This is chemically impossible. Exposure to the anaerobic bog would preserve her body, and the peat would most definitely tan her skin, yet the acid in the peat (a pH near to vinegar) would also dissolve the calcium phosphate of her bones. Her bone structure would melt into a blobby mess, and her body would have the shape of discarded clothes or a shed snakeskin. And the body itself, once uncovered and exposed to the elements, would decay rapidly--making any postmortem inquest very imprecise.
It is a post-Christian belief that pagan practices are malevolent in nature. Human sacrifice, while easily recognized as barbaric today, would have been considered a mainstream rite of religious supplication by contemporary Celts or Norse, much like a Catholic today views penance or contrition. The offerings in these sacrifices were most often venerated. Bog bodies have been discovered in fine clothing, with well-kept hair and nails, and most of them were fed well as the contents of their stomachs were also preserved. Finally, many sacrificed offerings were volunteers. These rituals were performed with the belief that the sacrifice would appeal to the deity and grant the people divine favor. This would have been seen as the greater good, and the sacrificial deed as a noble, honorable action. The idea that ritual sacrifice is a devilish practice associated with infernal mysticism is a Christian anachronism applied after the fact.
During the party at Richard Guthrie's home, a piper is playing while haggis is served. Both bagpipe and haggis are common in Scotland, but absent from the traditions of Shetland islands. In fact, the haggis used in the movie seems an industrial product, rather than a traditional one.
Pagan sacrifices in the method of Norse or Celtic bog rituals did not eviscerate the corpse of the offering. This would be seen as robbing the gods. Most wounds found on bog bodies indicate the offerings were most often strangled. The Tolund Man, perhaps the most famous bog body, was found with the ritual garrote still around his neck.
A doctor should be able to tell the difference between insulin and an experimental male contraceptive. Diabetics must inject multiple times a day, and usually always during mealtime.