Plot hole: When talking about rescuing the kids, Carter mentions them in the plural. But so far, all they have to go on was Zoe's birthday, so they wouldn't have known that anybody else was there, and Thorne also had not said anything about Zane.
What Goes Around, Comes Around - S3-E18
Plot hole: Tess sends Jack an airline ticket to visit her in Australia. The ticket reads 'From: Eureka, Oregon, To: Sydney Australia.' Seems odd that a commercial carrier would have a terminal in the most secret town in America. Eureka is a town created by the US government for its top scientists to experiment with new technologies. It is made nearly invisible from the outside by giant holograms. Very few non-residents even know of its existence.
Suggested correction: There's nothing to suggest Eureka has a terminal open to the public or other commercial airlines. In fact, the airline is named CircumGlobal which is probably not a coincidence that it shares part of its name with Global Dynamics. It could be a private airline only for Eureka staff and citizens.
This One Time at Space Camp... - S4-E18
Plot hole: When Dr. Hughes is racing to save Allison when he thinks he is Carter from the events that happened in "I'll Be Seeing You" Henry says he is racing for a cliff, and that the cabin was just a hologram. But in the episode the Cliff was the hologram disguising the cabin. Henry even commented in that episode that he did not remember a cliff being there.
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.
