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.
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 (Kissed by Fire (2013)).
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 (Walk of Punishment (2013)). However, the simple truth remains that if Jaime hadn't intervened on Brienne's behalf and started that conversation, his hand would not have been cut off.