The official words of House Lannister, which Bran failed to remember, are "Hear Me Roar!". Maybe the reason is that they are mentioned so rarely both in the books and the show. "A Lannister always pays his debts" is their unofficial motto, which is mentioned much more often.
The bloody encounter between Eddard Stark and Jaime Lannister is significantly different than in the novel. According to the novel, it was raining; Eddard and his men were riding horses, not on foot; they encountered the Lannisters on the way back to the Red Keep, not when exiting the brothel; Jaime did not participate at all in the fighting, but told his men to kill Eddard's guards, then left; Eddard was not speared by one of the Lannister guards, but broke his leg when his horse fell.
Renly states that he is the fourth in line of succession, following Joffrey, Tommen and Stannis - omitting Myrcella and Shireen. It is not a mistake, since according to the royal succession laws of Westeros, female heirs are behind all possible male heirs. Thus a king's daughter is behind both younger brothers and uncles.
Maester Luwin, Ros and Theon mention the Greyjoy's Rebellion that took place nine years before the beginning of the series. The rebellion was crushed and Balon Greyjoy (Theon's father) was forced to surrender to Robert Baratheon.