Barrow makes a pass at Mr Pamuk, and Pamuk ties his tie in the mirror afterwards. When he's done, it's obviously tied incorrectly, yet when he turns to face Barrow it's now tied perfectly.
Mrs Hughes is carrying things when she sees a pained Bates in the servants corridor, but after their conversation when the shot widens out she's not holding anything.
After Cora gets up from the bench during her conversation with Mary about Evelyn Napier's visit, her coat is alternately buttoned and opened.
When Lord Grantham was dressing for the dinner after the hunt, he wore an off-white waistcoat and bow tie with one pointed end, but during the dinner his waistcoat and tie were white, and the latter had two straight ends.
Given that Downton is a large estate house in the vill at which the fox hunt was held, it is odd that the family would have played no role if not for their invitation of Mary's suitor Napier. In reality, the family would likely have been hosting more than one noble friend or extended family member at the house, with the hunt being a major diversion for the family, locals and house staff.
In 1912, an Ottoman Turkish diplomat is introduced as Mr Kemal Pamuk. The Surname Law of the Republic of Turkey was adopted on 21 June 1934. Before then, Turks carried titles such as "Pasha", "Hoca", "Bey", "Hanim", "Efendi", etc., rather than surnames in the European sense.
At the hunt, the riders and dogs cross a stone bridge over a modern asphalt road. While paved roads could be found in large cities such as London, it was impossible for a country estate like Downton to have those in 1913.
When Kemal and Lady Mary were at the dinner table discussing dentists, Kemal suggests that Mary visits Istanbul. He should have said Constantinople, as it was only renamed Istanbul in 1923.
As the hunting party crosses the stone bridge on horseback the top of a modern car can be seen speeding by on the road in the background.