Episode #1.4 - S1-E4
Factual error: William plays a bit of music on the piano - the tune is called "After You've Gone", and it was written in 1918. This episode is set in 1913.
Episode #1.2 - S1-E2
Continuity mistake: When Cora (Lady Grantham) goes to Violet (the Dowager Countess)'s house to discuss Matthew and Isobel Crawley, she sits at the table and takes off her gloves shown in a shot from the front, and then the shot changes to over her shoulder and she is seen taking the same glove off again. (00:37:25)
Episode #1.1 - S1-E1
Other mistake: Lord Grantham tells Violet that he wanted to put 'lights' in the bedrooms but Cora did not, but at the end of the episode just before he blows out his candle Cora turns and off camera turns off a light that "clicks."
Episode #1.1 - S1-E1
Continuity mistake: Near the end of the first episode, when Robert Crawley gets into bed he first puts his candlestick down on the nightstand. Then it disappears. Then when he's in bed and ready to blow out the candle, it's suddenly back again.
Episode #1.7 - S1-E7
Continuity mistake: Near the end of the episode with the garden party, there is a scene where Edith is pleading with Anthony Strallan not to leave. You can see Lady Grantham lying down on a lounge chair in the background, with a man who is distinctively Lord Grantham standing next to her talking to her. But the scene immediately cuts to Lady Grantham, her maid O'Brien walks over and Robert is nowhere to be seen.
Episode #1.3 - S1-E3
Factual error: The Turkish character "Kemal Pamuk" is given the surname "Pamuk." However, surnames weren't used in Turkey till mid-thirties. Yes, Pamuk is a real Turkish surname but no Turk would be using surnames in 1912.
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