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?
You Gotta Not Fight for Your Right to Party - S2-E6
Plot hole: When Miley (as Hannah) gets stuck in the truck while trying to escape, she tells Jackson that her "belt's caught". But, when Jackson rescues her, it is visible that she is wearing no belt.
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.
Plot hole: The Unit discovers a soldier who they think is Betsy, tied to a chair. They note that the room is covered with PIRs or Passive Infrared Sensors. They then take out their night-vision goggles and begin counting the number of "infrared lines" they see. However, PIR sensors don't emit anything; they are passive. (00:23:15)
Plot hole: When Mr. Ballentine is telling Emily about her assignment, he sets the blue folder down near his side of the desk before he gets up. Then we see Emily pull it across the table and quickly peek in it. When Ballentine turns around, the folder is still close to Emily, which shows that she at least tried to look in it, yet Ballentine says nothing about it no longer being in the spot where he set it down. If Emily thought that it was okay for her to look in the folder, she wouldn't have waited for Ballentine to turn around before she touched it.
Plot hole: Owen is unable to give Henry the kiss of life as he has no breath, and yet he is able to talk.
The Amazing Psych-Man & Tap Man, Issue No. 2 - S6-E4
Plot hole: The flashback involves Young Shawn and Gus getting ready to go to a comic book convention, Shawn in costume, with his father's consent. This contradicts the flashback in "Shawn Vs The Red Phantom," where Henry won't allow Young Shawn to even read comic books or play superhero with a towel around his neck.
Remember the Monsters? - S8-E12
Plot hole: A couple episodes prior, Deputy Marshal Clayton stated that he shared Hannah's picture everywhere after receiving a tip that she may be in Miami. In the same episode, Hannah was spotted at a hospital and Clayton was called in about it. This should have only increased public awareness concerning her, but at the beginning of this episode, she somehow made it through airport security and all the way to her gate before spotting Elway and hiding from him in the ladies room.
Plot hole: Cleo's photo album contains photos of her and Lewis from past episodes ("Love Potion", "Doctor Danger" and "Hocus Pocus"). It's impossible that their photos could have been taken because they were alone in all of them. (00:03:07)