Revealing mistake: The money that Micah dumps out of his backpack is very obviously fake. In fact, the $20 bills have Benjamin Franklin's portrait on them.
Continuity mistake: After throwing the laptop, when Mohinder takes the key out of the book, the tape is bunched up and stuck to the key, but in the next shot the tape is fresh and sticking out freely.
Continuity mistake: When Hiro gives Charlie the Japanese phrase book, Charlie flips the book over to look at the back cover, then flips it frontwards again. In the next shot, she's instantly looking at the back cover again. (00:16:20)
Continuity mistake: Mohinder and his friend enter Sylar's apartment. He's wearing a white shirt. In one shot, when he finds Sylar's secret room, he is wearing a dark jacket.
Suggested correction: It's not a dark jacket. It's still his shirt but since he's in the shadows, it just looks darker. You even see when the light swings you can catch a glimpse of the shirt.
