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."
How to Stop an Exploding Man - S1-E23
Deliberate mistake: At the plaza, Peter tells Claire to shoot him because there is "no other way". Nathan then comes flying in and declares, "Yes, there is, Claire!" However, Nathan could not have heard Peter and Claire from the distance he flew in and the rushing of air past his ears.
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.