When Rupert walks Into the room after Jamie and Claire kill Dougal he is holding the knife above Dougal's body. In the next scene you hear him pulling the knife out.
Brianna could not have been going to Harvard in 1968: They didn't admit for another nine years.
When Roger tells Brianna that he detects an American accent, she corrects him that it's Boston. But she has no trace of a New England accent, whatsoever.
Sophie Skelton's real life British accent peaks through in some words especially when Clare tells Brianna about Jamie.
The gray in Claire's hair sometimes is more, sometimes less, sometimes not at all.
When Brianna meets Gillian she says that Richard the Lion Heart was a King that knew how to take care of his people. He however did not. Of his 10 year reign he spent only a couple of months in England and when he was taken captive during a Crusade Hugh taxes were imposed on the English people to get him free.