When Nymeria rushes to Myrcella, she is holding a whip. Next shot, she is holding a dagger.
Doran Martell, when speaking about Myrcella and Trystane, refers to them as "a Lannister and a Martell". While Myrcella is technically born to one (or two) parents of the house Lannister, politically she would be regarded as a Baratheon.
Cersei tells Littlefinger that Winterfell is "a thousand miles" from King's Landing. But in Baelor (2011) and in the books, it was mentioned that the distance between King's Landing and the Wall is around a thousand leagues. Winterfell is close to the Wall, within a couple hundred miles at most, which means it should be located more than 2,000 miles away from King's Landing. However, this is not necessarily a continuity error: the phrase "a thousand leagues away" is often used in the novels to indicate a very long distance figuratively.
Sansa is persuaded by Littlefinger to marry Ramsay, which she does in this episode. This plan doesn't really make sense for any of the characters involved: Littlefinger loses control of Sansa, who is not only "the key to the North" but also the object of his affection/obsession as a replacement for her mother Catelyn, whom Littlefinger was in love with; Sansa agrees to marry the Boltons to "avenge her family", but by doing so she considerably strengthens the Bolton's legitimacy in the North by merging them with the popular Starks; the Boltons essentially accept to commit treason against Cersei, for whom Sansa is a wanted regicide. In the novels, Ramsay marries Jeyne Poole (one of Sansa's friends) posing as Arya, which makes much more sense as: 1) Jeyne is forced into the marriage and has no way to refuse; 2) Littlefinger loses nothing, as Jeyne herself has no personal or political value to him; 3) the Boltons solidify their position by marrying a fake Stark, but do not risk angering the Lannisters, who are aware of the deception.
In a shot from behind Lancel, showing him speaking to Littlefinger, his mouth is clearly speaking many words emphatically, but no sound comes out.
Loras is charged with sodomy on the strength of the testimony of Olyvar, his supposed squire, who bolsters his testimony by mentioning a birthmark on an intimate part of Loras' body. However, a squire's duties would include dressing and undressing his master, providing plenty of opportunities for him to see Loras naked in a non-sexual context.
Arys Oakheart of the Kingsguard, who escorted Myrcella to Dorne, was supposed to stay at her vicinity and protect her. No explanation is given to his absence at the time the Sand Snakes attacked Myrcella.
Even if knowledge of the birthmark was enough to incarcerate Loras, it wouldn't work as proof that Margaery knew about Loras' relationship with Olyvar.
Tyrion tells Jorah about his father Jeor's death, although he has never been informed about that.
Ramsay and Sansa are married, but she is still married to Tyrion. Although that marriage could have been annulled, as it wasn't consummated, there is no suggestion that was done.