Goofs

The Farnsby's house moves between seasons. In season 1, when they first meet Sam and Jay, they introduce themselves as the next-door neighbours, and talk about hearing the construction work from next-door. But in season 2, Sam says they are two doors down. With the size of the grounds belonging to the houses, two doors down would be several miles away, and completely unaffected by anything Sam and Jay did with their house.

The wounds that killed some of the characters appear and disappear between episode, in particular Flower's open gash in the back and Nigel's chest wound. Also, the basement ghosts appear in Season 1 with pustules and wounds, more consistent to the appearance of the plague ghosts in the original BBC version, but not with the cholera epidemic that killed them in this one. This is corrected in Season 2.

Denmark didn't exist as a country when Thorfinn was alive, so there were no Danes for him to kill, torture, or irrationally hate.

Al Capone left New York in 1919, Alberta couldn't have known him in the 20s.

There was no such thing as an overweight poor person in the 1920's. Or for most of history, which is why it used to be a sign of wealth and a standard of beauty. Since Alberta's weight is brought up in the show, it highlights the mistake. Her weight was addressed, so there should have been some kind of explanation. It was not possible to even buy clothes for someone of her size because people just weren't as big then.(The maximum size on dress patterns was the equivalent of a modern size 10-12 UK.)

Vikings came from Scandinavia, Scandinavia includes Denmark, Vikings had no particular prejudice against Vikings.

There are no such things as ghosts.

Everyone seems completely unaware of World War One, despite it happening during Alberta's lifetime, only a few years before her death. The Roaring 20's were essentially the victory party, so at the very least, Alberta really should have noticed that the country went to war in 1917. Hetty really should have noticed her male descendants going off to fight, (and being conscripted in WWII) as well.