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.
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.