Continuity mistake: When Jack, Stark, and Allison walk into the room at G.D. where Martha escaped from Stark is seen putting his hands on his hips twice.
Continuity mistake: When Jack is using the mustard to find Martha, Vincent ducks behind the counter. The shot changes to show just Vincent and he is shown ducking down again.
Best in Faux - S3-E3
Continuity mistake: Henry is showing Zoe how to melt a penny, but in the next shot the penny is not melted.
Best in Faux - S3-E3
Continuity mistake: When Dr. Mendel picks up the beaker with the blue liquid it is almost full, but when he goes to pour it out the beaker is almost empty.
Continuity mistake: When Henry is carving Dr. Nathan Stark in the wall, we see him carve the H and the wall says DR. NATH. As Jack is walking in an A appears after the H.
Other mistake: Captain Eureka losing his finger makes absolutely no sense. He doesn't cry out in pain, there's no blood, and where the finger ended up is completely illogical. The finger didn't just sever on its own; it's shown that severing only occurs when passing through objects. Captain Eureka goes through a wall that is a good fifteen feet away from where the finger is discovered, and it is implausible to think it could have rolled there on its own.
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.
Factual error: Zane used ULF (Ultra Low Frequency) to communicate with Henry and notes he can "only send numbers." This is a reference to extremely low bandwidth of maximum 300 Hz transmission. However, later Henry magically creates an upgrade that allows voice communication - not possible with ULF. Also, no way Sheriff's old radio would pick up ULF band communications in the first place.
Continuity mistake: When Jack and Lexi are in the jeep talking a car can be seen in the mirror, but when they pull over no car passes them.
Continuity mistake: When Captain Eureka puts out the fire at the pumping station, Jack's Jeep somehow gets on fire, but we are able to see where the fire went, and it didn't come anywhere near the road or the Jeep.
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.