Episode #4.1 - S4-E1
Other mistake: They act as if Carson's friend Charlie has his first appearance in season 4 episode 1, but in an earlier season and episode he arrived at Downton Abbey and caused a scene in the library trying to extort money.
Episode #4.4 - S4-E4
Character mistake: When everyone is preparing to go in to dinner, Robert is wearing an adjustable bow tie. It's bad enough he's wearing black tie to dinner when he has guests, as his mother points out, but Robert, the Earl of Grantham, absolutely would not be seen wearing an adjustable tie with a stand up shirt collar, even among only his immediate family. (00:35:15)
Episode #4.5 - S4-E5
Factual error: When Lady Edith visits a Harley Street doctor his nameplate is shown outside his surgery. His name is prefixed with "Dr." However, one of his post-nominal qualifications is "FRCS." As a Fellow of the Royal College of Surgeons, his name should be prefixed with "Mr.", as with all qualified surgeons in the British Isles.
Episode #4.7 - S4-E7
Factual error: When Edith goes to have an abortion, you can hear a Eurasian Collared Dove singing, but that species did not exist in Britain before the 1970s.
Answer: Lord Sinderby purchased the house, furnished and appointed, from someone else, complete with staff that come with the home (some of whom aren't happy to be working for a Jewish family). He bought the title, as well. If the artwork featuring Jesus is valuable, he might keep it. Also interesting, his ancestors Anglicized their name, though he is proudly Jewish.
Michael Albert