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.
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.
Al Capone left New York in 1919, Alberta couldn't have known him in the 20s.
Denmark didn't exist as a country when Thorfinn was alive, so there were no Danes for him to kill, torture, or irrationally hate.
On Pete's scout uniform, he has a United States flag patch on his right sleeve with the field of blue facing the rear. While a right sided flag patch does exist, this particular patch should be worn on the left side which is significantly more common.
Vikings came from Scandinavia, Scandinavia includes Denmark, Vikings had no particular prejudice against Vikings.
Nigel mispronounces "lieutenant" as "lootenant" every single time he says it.
It's "lootenant" in the US because they mispronounce all French root words, reading then phonetically, but in English it's pronounced "leftenant" from the original French "levtenant". No Englishman would get it wrong, especially not one from before the US invented its own version of English.
In fact, in the Revolutionary War both sides were British, so they all said "leftenant", which means Issac is saying it wrong too.