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: 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.
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.
Are You...? - S7-E1
Plot hole: It's out of character and against his code for Dexter to kill Viktor at the airport. Airports have security cameras everywhere (you can see one on the ceiling when he is wheeling Viktor into the unclaimed baggage storage), and using the unclaimed baggage storage as the kill room is equally unwise, because any airport employee could walk in at anytime and catch him red-handed. Dexter was caught murdering Travis Marshall by Deb just hours before, so if anything, he should be even more cautious.