Terra Nova - S1-E6
Continuity mistake: The bike wheel is first shown spinning counterclockwise, as expected from the previous shot, but then it rotates clockwise in the next shot. (00:06:44)
Continuity mistake: In the scene in T'Pol's quarters, after she and Tolaris have mind melded and she asked him to leave, he walks out, and the door starts to close before the shot changes to T'Pol. But when the shot changes, the light from the door on T'Pol shows the door still opening, and then closing. (00:33:40)
Continuity mistake: When Hoshi returns to the ship, Archer says in his log that Trip and Malcolm are taking her back to Enterprise. Trip wasn't on the planet: the landing party was Archer, T'Pol, Hoshi, and Malcolm. (00:11:20)
Plot hole: In 'Oasis,' several times in the episode, specifically when they took Trip captive, the holograms appeared out of nowhere brandishing weapons. The holograms can walk through walls, which we saw, but the guns were real. We saw them hit the deck when Liana deactivated the holograms. So how did they appear with the guns? (00:34:00)
Fallen Hero - S1-E23
Other mistake: As Archer, T'Pol and the ambassador are having dinner, the Ambassador inquires about who previously occupied the cabin (that she was to be staying in). T'Pol assumes this is regarding concerns about human "odor", but the ambassador says, "Actually I was hoping to meet the crew member in order to thank her for allowing me to disrupt her routine." However, the ambassador has no way of knowing what gender the crew member is, as no mention of this person has been made. Although the crew member was, in fact, Hoshi (who is female), the ambassador would not have known this, and had no reason to refer to the crew member as "her". (00:08:34)
Suggested correction: There are any number of ways the ambassador could know. Considering the ambassador knew it was a crewmember's quarters, it's likely that when she came on board, the pronoun "she" was used in reference to the prior occupant. Or perhaps an item of clothing was left in a drawer.
Additionally, in our culture if a gender is unknown a male pronoun is frequently used, but her culture may use a feminine pronoun as the default.
Continuity mistake: Archer, T'Pol and Trip enter the cloaked Suliban ship, after Trip uses the stun grenade. Archer exits the docking bay first, followed by T'Pol and finally Trip, however in the next shot Archer and Trip are together and T'Pol exits for a second time. Also as she exits the door closes behind her, but in the following shot the door closes again. (00:28:00)