Continuity mistake: When Peter and Claude are invisible and walking in New York, just after Claude has released his hold on the T-shirt rack, they bump into a man in a coat. Cut to a different angle, showing the two on camera, and the man in the coat is gone. Instead there are two girls and a man with glasses walking directly behind Peter and Claude, none of whom were there a split second ago. (00:02:05)
Continuity mistake: In the scene where Sylar and Mrs. Bennet begin to talk, she becomes suspicious about his interest in Claire. When Mrs. Bennet picks up the phone to call her husband, Sylar visibly moves his finger to use his telekinetic power right before the angle changes. In the next shot, Sylar again does the same motion with his finger, but this time the phone is removed from Mrs. Bennet's hand.
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 ★