Deliberate mistake: The newspaper that shows Petrelli's victory has repeated paragraphs through the article. The article seems to be composed of three paragraphs. One paragraph starts with "I was," and two paragraphs start with "The."
Revealing mistake: Claire Bennett is accidentally tackled when she and Zach are arguing while watching the football game. Apparently, her neck is badly broken in the fall, even twisted a full 180°. However, if you watch closely as she falls, you can see that she is completely fine, stretching out her arms to take the impact before rolling around. She lands on her front, arms stretched out, all in all well prepared for the landing, and rolls around. In the next shot her neck is twisted in a way that simply wouldn't be possible in such a fall. She would have had to have her head stuck under something before rolling over, which she certainly did not. The guy tackling her did not land on top of her either. (00:19:40)
Other mistake: When Niki looks at the Cadillac's registration, it says the license plate number is "307RTH." When she opens the trunk, you can see the plate and it's "329OCX."
Chosen answer: It's not been made 100% clear. It was originally assumed that he actually consumed part of the brain, but this has turned out not to be the case. Sylar has been shown all along to have an instinctive knowledge of how things work and how to fix them - this is his actual original power and the ability that made him an exceptional watchmaker and repairer. It appears that he uses a similar process when acquiring new powers - he exposes the brain of the target, allowing him to examine it and determine how their power functions. He can then apply that knowledge to his own brain, allowing him to replicate the ability in question.
Tailkinker ★