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.
Plot hole: Dillon was quickly identified by the city sensors as having metal parts, thus classifying him as a threat to the city. Yet Tenaya, who is essentially a cyborg, tries out for the Green Ranger without setting off the same sensors.
Suggested correction: Tenaya wasn't caught because the guards assumed the equipment was faulty. It was giving positives all day because of all the sleeper agents we find out about later.
The Feminum Mystique: Part 1 - S1-E5
Plot hole: If her younger sister Drusilla is sent from Paradise Island to retrieve Diana, how did she get to Washington DC or wherever, she had no way of knowing where her older sister would be.
Plot hole: The nuclear explosion is on Liberty Island, a small yield, but nonetheless big enough to move an enormous amount of water towards the coasts on all sides. When we see Sertrakian and the others at the harbor no water is heading their way - they should be washed away by it. (00:37:30 - 00:38:45)
The Beacon - S1-E26
Plot hole: Barrows introduces himself as "Dr. Dennis Barrows," and Teddy asks, "What's a doctor?" As the isolated villagers have never heard of doctors, Teddy would have no way to know that "Doctor" was a title/profession and not simply part of Barrows' name. He should have asked, "What kind of a name is Doctor?"