Point A. Eragon comes across the egg while hunting, a plot factor that reflects a lot of fantasy: living a normal life until you come across something abnormal. I'm not saying that's a bad thing, but I would rather have the story begin with Eragon being familiar with dragons, and maybe even opening the novel with Eragon already training Saphira.
Point B. Eragon is too trusting. Correct me if I'm wrong, but Eragon seems very accepting of Murtagh and Arya. The latter is not an issue, but *spoiler* Murtagh turns out to be a traitor. Eragon has entered the world of dragons and Riders, he should watch out more.
I am also aware of the heavy similarities between 'Eragon' and the Lord of the Rings and Star Wars. I'm not a big fan of either of those, but after reading through the similarities, and reading of how the author is the son of parents that made their own publishing firm, I think Paolini was very conscious of his choices, and should've taken the time to tweak them, and make them less noticeable, if they were to remain in the story at all.