Continuity mistake: When Chris has a gun aimed at Evelyn he's holding it with his right hand. A shot behind him and suddenly it's in his left hand.
Audio problem: When Carrie Fisher and David Soul make out in Trieste, a performer at the local restaurant is supposed to be singing the popular Italian song "Torna a Surriento", but his lips barely even move and it's self-evident that he's not the one singing. (00:11:30)
Other mistake: Christina suggests that they have found Atlantis. However, they start in Hawaii, which is in the Pacific. The general consensus is the Atlantis is in the Atlantic (or Mediterranean) and not the Pacific. Some people do suggest that the lost continent of Mu is in the Pacific.
Revealing mistake: When one character's killed, stomach sliced open, you can see the wire yanking open the prop stomach to the left of the camera.
Visible crew/equipment: When Guarino is being taken away by The Hunter, you can see the rope used to pull him in the upper right corner of the screen. (00:46:05)
Revealing mistake: When Jemma enters the headshrinker's laboratory, there is a table with three heads on it each encased in glass. When it goes in close-up on the middle head, you can see that the table has a hole where the actor can slip in his head.
Continuity mistake: Clearly a different guy playing Zack in the beginning as he looks to be over six feet tall and has a full head of combed back brown hair. Zack later on looks like he's only 5'5" with receding brown hair.