Plot hole: If Noah could be brought back from the dead with Claire's blood why couldn't they bring back Nathan? Was turning Sylar into Nathan really the first thing they could think of?
Revealing mistake: In the scene after the fire, when Kyle is playing with a candle, as he picks up the candle his belly button is visible. It has been established that Kyle has no belly button, therefore this is a mistake.
Children of Earth: Day One - S3-E1
Revealing mistake: When the children are possessed by the 456, they're supposed to be frozen and stare blankly ahead. But during the second possession, as the camera is panning across a school playground, a boy on the far right is looking directly at it. As it moves closer to him, he swivels his eyes back to where they're supposed to be. (00:16:30)
Continuity mistake: Just before the robbery, Jake throws some water bottles and a flashlight over a small mound into the bushes, to hide them from the thieves. But when Mimi later picks them up, they are much closer to the truck, and on the other side of the mound. In fact, the bottles and flashlight would have been in plain sight for the robbers where she picks them up.
In Too Deep - S5-E8
Plot hole: Carter is apparently just learning about Feynman's Day, which Allison explains as "Eureka's version of April Fool's Day." It's highly improbable that Carter could have lived in Eureka for five years and still be oblivious of this, especially given all of the hijinks that happen.
Continuity mistake: When the bad guys create a roadblock with their 2 cars as Hopper drives his girlfriend to her mother's house, the cars stop with one on one side of the yellow line, and the other stops with the steering wheel over the line. The camera angle changes, and now both cars are neatly, evenly positioned, with their engines sitting over the line. (00:02:05)