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: Hiro's powers are still quite unreliable, and a locked closet door isn't a huge obstacle. Since Hiro knows he needs to rescue Ando, it's probably safer to try and bash the door down than risk teleporting to the wrong place or time.