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)
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.
Continuity mistake: Mary has written a letter to Matthew. We hear her voice reading the text, which begins: "So there we have it. I look forward to introducing the two of you, just as soon as you are next at home..." Next, when the page of the letter is shown, it reads "...happy to hear - come to pass. I look forward to introducing you to Sir Richard, just as soon as you are next at home." (00:11:03)