According to the novel, while Daenerys was at the House of the Undying, she saw no vision of Khal Drogo with their stillborn son Rhaego. She saw various visions about the past and foreshadowing of future events, and heard obscure prophecies.
According to the novel, Mandon Moore's blow disfigured Tyrion much worse than in the TV series: in addition to the scar which runs across Tyrion's face from above one eye down to his jaw, most of his nose was sliced off.
According to the novel, it was not Littlefinger but Dontos who explained Sansa that Joffrey's betrothal to Margaery Tyrell would not stop him from having his way with her, and promised to take her home.
The scene of the beginning of Jaime and Brienne's journey to King's Landing is not included in the original novel, but in the sequel "A Storm of Swords". Robb's marriage also takes place in "A Storm of Swords", but off-screen since Robb is not a point of view character.
Season 2 is currently the only season of the show to credit Nikolaj Coster-Waldau lower then Lena Headey. Every other season he is credited higher than her in the opening credits. Similarly, Isaac Hempstead Wright is credited higher than all of the Stark siblings (excluding Jon Snow), whereas for most of the series he is credited lower than his siblings.
The trivia items below may give away important plot points.
According to the novel, Daenerys saw at the House of the Undying a vision of a man that looks like Viserys but taller than him, whose eyes are dark indigo rather than lilac (presumably her late brother Rhaegar Targaryen), stating "The Dragon has three heads". This saying is commonly believed to imply that there are two live Targaryen descendants in addition to Daenerys, and the three of them will be united and eventually take over Westeros.
Among the prophecies Daenerys heard at the House of the Undying is "Three treasons will you know... once for blood and once for gold and once for love". Daenerys believed Mirri Maz Duur committed the blood treason by causing the death of Khal Drogo and her unborn son Rhaego. It is unclear whether the gold and love treasons were or will be committed, and by whom. The love treason, however, may refer to Ser Jorah Mormont, who is revealed in Game of Thrones: The Mountain and the Viper (2014) to have once been a spy of Robert Baratheon. Although he admits to it, he maintains his loyalty and love for Danaerys. Mormont's secret feelings of love for Daenerys are well known, making him a potential candidate for the prophecy.
According to the novel, Daenerys saw at the House of the Undying a vision of feast of slaughtered corpses, among them a dead man with a wolf's head sitting on a throne wearing the iron crown. Clearly this is a foreshadowing of the Red Wedding, which occurs in the novel "A Storm of Swords".
According to the novel, Robb breached his pact with the Freys by marrying Jeyne Westerling (whose character is replaced in the TV series by Talisa). Robb was injured in the successful attack on the Crag, and soon afterwards he was informed about the alleged death of Bran and Rickon. While he was lying in bed, injured and emotionally devastated, Jeyne came to comfort him, and they made love. In the following morning, Robb felt compelled to marry her, to protect her honour. When Catelyn learned about the marriage, she explained to Robb what a terrible mistake he had committed and he admitted that, but it was too late. As Catelyn predicted, the marriage led directly to the break-up of Robb's alliance with the Freys, and they angrily took their forces back. Robb's army was significantly weakened as a result.
According to the novel, Roose Bolton's bastard Ramsay was caught by Rodrik Cassel and imprisoned in Winterfell, disguised as his servant Reek, shortly before Theon conquered it. After Theon took over Winterfell, he released and accepted Ramsay to his service, unaware of his true identity. Ramsay was the one who suggested to kill the two kids as cover-up of Bran and Rickon's escape. After Theon's sister left Winterfell without bringing reinforcements, Ramsay offered that he would go to recruit soldiers, and Theon agreed. Ramsay brought about 600 men from Dreadfort, and treacherously killed Rodrik Cassel while the latter was besieging Winterfell. Then he and his men proceeded to burn Winterfell to the ground, killing most of its residents and Theon's men. Theon and several others were taken captives to Dreadfort. When Roose Bolton reported to Robb, he falsely claimed that the Ironmen destroyed Winterfell, and that his son captured Theon and saved the survivors. Theon's fate remains unknown till the fifth novel "A Dance with Dragons".
According to the novel, Maester Luwin advised the Stark boys and their escorts to go on separate ways for their safety, and they followed his advice: Bran, Hodor, the Reeds and Summer went north beyond the Wall to find the three-eyed crow; Osha, Rickon and Shaggydog went to Skagos, the cannibals island.