Jamie's hair is both significantly longer and redder when he and Claire get to France than when he and Claire left Scotland, even though it had not been that long since they had left.
As a nurse Claire would know that cloth can be infected with smallpox so cuddling up to Jamie after wiping her hands on her clothes could have infected him.
Claire tells Mrs. Graham that she once called Jamie a "fucking sadist" and he didn't understand the term. In The Reckoning, she calls him a "fucking bastard" when they have the fight near the river, and then later in that episode when he spanks her she calls him a sadist.
When Claire is telling the story where she called Jamie a fucking sadist in season 1, she says he didn't know what that was. The word fuck was first recorded in the 14th century. It was first used as a noun in the 17th. The word sadist doesn't appear until much later. But given Jamie's travels and who he kept company with, it's hard to believe the word fuck never came up.
Frank, after hearing that Claire is pregnant with Jamie's child, goes to the potting shed and grabs a pot off the shelf. The pot breaks as he is pulling it, before he actually smashes it and destroys the rest of the shed's contents.
The only TWA plane of the era to have square windows was the Martin 404, which did not enter commercial service until 1950, two years after the date in which the episode takes place. It would not take Frank two years to accept a post at Harvard.