The tartan pattern on Mac's kilt changes between being at the party at Salinger's and when he walks the family home that night.
The newspaper article that Brad and Lindsey find about their mother's birth states that her parents were the 12th Duke and Duchess of Glencrave. But at the Christmas ball at the end of the movie, Josephine calls her late brother the "11th Duke of Glencrave." He should've been the 13th.
When Lindsay takes Mac to the doctor, the sign on the building is 'Medical Center' this is incorrect as the British spelling is 'Centre'
During the ball, the flute player is holding her flute in the wrong direction.
This movie misrepresents the rules of inheritance of noble titles, i.e. sisters do not inherit noble titles ahead of their brothers, nor can a brother and sister both inherit the titles of duke/and duchess. A female does not inherit the title of duchess except in very rare and special circumstances and such cases must be approved by the monarch. Also, multiple children cannot have titles beyond that of Lord or Lady.
During the tour, Hamish says the castle dates back to the 14th century, but then two minutes later he says the castle was built in 1491 (which is the 15th century).