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.
Revealing mistake: When Carter and Jo almost crash into the reflective smart dust wall on the road, Carter puts his hand up and waves it, to see his mirror image doing the same. Carter's mirror's hand movements are out of sync, which reveals that the "mirrors" are the actors, and the "real people" are doubles.
Other mistake: When Zane and Andy get on the elevator, Jo is there to zap Andy. We see Andy start to fall backwards, and then we hear a thud as if he fell to the floor. When the shot changes, he's propped up against the wall. But he was standing too far away from the wall to land against the wall in that position.
