Arya asks if dragonfire can stop the Night King. Bran answers "I don't know. No one's ever tried". Actually, during the Wight Hunt, Daenerys tried to destroy the Night King by dragonfire, and he was unharmed (Game of Thrones: Beyond the Wall).
Brienne claims that Jaime lost his hand because he protected her from being gang-raped by Locke's men. Actually, Locke cut Jaime's hand because the latter annoyed him by mentioning the wealth and power of his father (Game of Thrones: Walk of Punishment).
Sam tells Jon and Dolorous Edd that only the three of them are left from the Night's Watch members who were together in the beginning, mentioning Grenn and Pyp. Actually, Edd was not introduced until Season 2, and Pyp did not participate in the Great Ranging with the rest of them.
Daenerys says she was told that her brother Rhaegar had raped Lyanna Stark. No one has ever told Daenerys such a thing. On the contrary, Jorah Mormont and Barristan Selmy told her only positive things about her father and brother.
Jaime claims that everything he did (including the killing of Aerys) was for his house and his family. Actually, he did it to prevent Aerys from killing the residents of King's Landing by wildfire (Game of Thrones: Kissed by Fire).