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.
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.