Continuity mistake: At the waterfall, after jumping off the cliff and into the water, Skye leads Josh to the rock carvings. Josh's wet hair keeps changing position from being completely slicked back, to partially covering his forehead, to being completely forward over his brow.
Continuity mistake: When Casey Durwin deliberately stalls his motorized wheelchair in front of the Phoenix Group convoy (so Jim Shannon can slip into the last vehicle), his chair's position keeps changing. From the front angle, the chair is directly centered in the middle of where the truck is. When seen from Malcolm's view on the side, Durwin's chair is now partially clear of the truck's front end, then it's back in the middle.
Plot hole: Skye's mother, Deborah, was held hostage by the Sixers for several years, though everyone believed she had died in an epidemic and was buried in Memorial Field. The Sixers kept her alive with medicine only they had to force Skye to act as their spy. Even though Terra Nova has a medical clinic staffed by doctors and nurses, it was never noticed that no one had witnessed Deborah dying, her body was never placed in the morgue, that was there no record of her being buried, or even questioned that there was no corpse. Deborah just disappeared without a trace and nobody wondered about it.
Revealing mistake: Dr. Shannon identifies the skeleton as being a middle-aged male, but the skull is female. A male skull has a more pronounced ridge over the eye orbits, a sloping forehead, a longer mastoid process, and the skull widens at the back, unlike a female's that is more parallel.
Continuity mistake: When Skye, Josh, and the other teens reach the waterfall, Skye says she's taking the shorter (and more dangerous) route. After the others have have left to take the longer path, Skye strips down to her bikini, drops her outer clothes on the ground, then jumps off a 45-foot cliff into the water below, with Josh following her. When they meet up with the other teens shortly after, Skye is suddenly fully dressed again, even though her clothing was left atop the cliff, and her wet hair is now dry.