Visible crew/equipment: When Claire runs away from Bob after he calls her "Ms. Bennet", you can see Bob's shadow and another person's shadow on the ground. Since no one else was standing next to them, it has to be a crew member, most likely a camera man based on the odd shape of the shadow.
Continuity mistake: When Maya is arrested, she starts manifesting her powers on the policeman. In a close-up, we can see the black ooze coming out of her eyes. Cut to a shot from above, when the policeman's eyes turn black and he drops the handcuffs, and Maya's cheeks are suddenly clean again, with no trace of the black stuff. (00:33:45)
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 ★