According to the novel, it was Tyrion who planned Jaime's unsuccessful attempt to escape: he sent to Riverrun four people among Cleos Frey's escorts, whose secret mission was to free Jaime, and they nearly succeeded.
According to the novel, during Jaime's unsuccessful escape attempt, he killed two guards, none of them were Karstarks. Jaime killed two of Rickard Karstark's sons, Torrhen and Eddard, in the Battle of the Whispering Wood, before he was first captured.
Most of Catelyn and Jaime's conversation, as portrayed in the novel, was omitted from the show: Jaime's admission that he is the father of Cersei's children; his version about the dagger, which proved to Catelyn that Littlefinger lied to her about Tyrion being its owner; how Eddard's father and brother were killed by the Mad King.
There are no Alton and Cynda Lannister in the novels. Alton replaces Cleos Frey, Jaime Lannister's cousin (son of Tywin's sister). Cleos Frey was killed not by Jaime, but by outlaws on the way to King's Landing.
According to the novels, Jaime was a squire for Lord Sumner Crakehall, not for Barristan Selmy; he never had any squire named Brian; when he took part in the campaign against the Kingswood Brotherhood, he was fifteen years old, not sixteen; and he never competed against Balon Swann.
The trivia items below may give away important plot points.
According to the novel, Bran, Rickon and their escorts (the Reeds, Hodor and Osha) never reached the farm, and did not leave any food leftovers anywhere. They reached the edge of the woods, sent the wolves on to mislead the pursuers, then returned to Winterfell and hid in the underground crypts till the castle was destroyed by Ramsay Snow, Roose Bolton's bastard.
The kids that Theon had tarred and hanged were neither Bran and Rickon nor orphans, but two unnamed miller's sons. It was Ramsay Snow, Roose Bolton's bastard, who suggested that to Theon as cover-up of the Stark boys' escape. Theon accepted the advice, and had the boys and their mother killed. The kids were flayed, tarred and dressed in Bran and Rickon's clothes. Maester Luwin was the only who realized it was a sham, because he noticed the leg muscles of the kid who was dressed in Bran's clothes.
Tywin's comment to Arya that she should say "m'lord" rather than "my lord" if she wishes to pose as a commoner, is based on a similar comment of Roose Bolton to Theon in the novel "A Dance with Dragons".