Continuity mistake: (Season 2 Episode 2) Near the end, as the worms have died and exploded trying to spawn, a shot shows Cutter, Claudia and Stephen ripping the spawning worms from their bodies. Stephen is shown with one in each hand and another hanging on the right of his chest. In the following shot he is seen ripping one off his right chin, which did not have any worm on it in the previous shot.
Plot hole: (Ep. 5) The weapon Stephen finds in a desert is a H&K G36. He states that it's not a military weapon and is mainly a mercenary weapon. The G36 is used by several police and special forces units in the world, including the British SAS, which could suggest another nation's or British government branch's involvement. Comment was probably made to deepen the intrigue of the season plot.
Other mistake: In the last episode of season 3, Helen Cutter goes to site 333 to kill off the first hominids. Connor mentions that that's the site where thirteen members of a hominid family all died at once, and no one could ever figure out why. The implication is that it was Helen's actions that killed them off, and we see her doing it. Right after killing them, Helen herself is killed by a velociraptor, which also dies. Danny Quinn leaves their bodies there and walks away. Doesn't that mean that, when site 333 is discovered in the future, they would also find Helen's bones and those of the raptor? I imagine it would cause some confusion if the bones of a modern human and a velociraptor were found in the same strata and the same age as the earliest proto humans.
Character mistake: Referring to the US, Russian and Chinese governments, the admiral says that "Washington, Moscow and Shanghai" have been informed. The capital of China is Beijing.
Factual error: Many of the Royal Navy details are completely wrong. The submarine captain's cap badge is not that of the Royal Navy. "Midshipman" Leonard wears the insignia of a chief petty officer. "Officer" (not a naval rank) Neal wears the insignia of a petty officer. "Officer" Shaw wears the insignia of an able rating. The Flag Office Submarines is depicted as a full admiral, whereas in fact he was a rear-admiral and the position no longer exists.
Character mistake: The submarine captain says they have no "kitchen staff" on board. No naval officer would refer to a ship's galley as a "kitchen". It's a tradition thing.
Factual error: Matt says he was in the Royal Marines, to which the submarine captain says "you were in the army?" Any naval officer would know the Marines are certainly not Army.