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.
Remember the Monsters? - S8-E12
Plot hole: In order to elude Elway at the airport, Dexter fills a backpack with random items and leaves it unattended under a seat, and then tells a desk clerk that he saw Elway deliberately put the backpack there and walk away, which leads to security detaining Elway and the airport being evacuated. Airports have security cameras everywhere, so security would have reviewed the footage and seen Dexter was the one who placed the bag there. They then would have gone through all security footage since he entered the airport in order to deduce his identity and then located and arrested him.
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.
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)
Idol Curiosity/Home Is Where the Hurt Is/Aw, Shucks! - S1-E9
Plot hole: Idol Curiosity: When the ship is dragging Russell through the water by his intestines, Russell gets launched in the air by a coral reef, then he goes through a ring of fire. In order for this to have happened, the ship itself would have had to go through the ring, which is very impossible. (00:04:19)