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)
Carbon Creek - S2-E2
Factual error: Part of this episode takes place in the 50s, during a previously-unknown incident of Vulcans crash landing on earth. Modern twenty and fifty dollar bills are visible in the tip jar.
Carbon Creek - S2-E2
Factual error: The story takes place in 1957 (Sputnik is already in orbit). At the end, T'Mir sells her invention, which ends up being Velcro (technically hook and loop fastener). However, George de Mestral obtained the patent for Velcro in 1955, and by 1957 he had already expanded into the United States.
Continuity mistake: When Reed instructs Archer how to disarm the second arming mechanism of the mine, he tells him to turn the first component clockwise, but then Archer is shown turning it counter-clockwise. Then Reed tells him to turn the rest of the components counter-clockwise, but afterwards he must reverse the last component to keep the mine from rearming, which means turning it clockwise. But when Archer reverses the last component, he turns it counter-clockwise.
Audio problem: At the very end of the scene where Trip persuades Malcolm to help him look for the station's computer, he hands Malcolm the PADD. Malcolm taps twice on the PADD as if he's working on something but there's no accompanying sound effect.
The Seventh - S2-E7
Continuity mistake: When T'Pol enters Capt. Archer's room there is a napkin on his leg. It changes position in the next shot.
Continuity mistake: When Captain Archer is talking to Hoshi in her quarters, at one point he leans against the door-frame. In the next shot of him from that angle, he's no longer leaning, even though we saw him from behind and he didn't move. In the next shot, he's back to leaning against the door-frame.
The Catwalk - S2-E12
Continuity mistake: T'Pol says she has never been camping, but she went in "Strange New World."
The Catwalk - S2-E12
Other mistake: The Doctor states that sick bay is the most heavily shielded area of the ship but later in the episode he is trying to move all of his specimens to The Catwalk. If the sick bay is the most heavily shielded area then he would not need to move the specimens.
Cease Fire - S2-E15
Continuity mistake: Admiral Forrest says this is the "first time" the Vulcans have asked Earth for help. But they asked Earth for help in "Fallen Hero."
Other mistake: Just as Malcolm finishes opening the hatch on the alien pod, a graphical mistake appears towards the left side of T'pol's arm. It appears as if a section of the craft had been added with an overlay, which abruptly disappears as the cutting tool stops firing. (00:01:30)
Suggested correction: It doesn't disappear. It just falls into shadow when the cutting beam is turned off.
Revealing mistake: When examining the burnt human in sick bay, the body moves his eyelids towards the end of the camera zoom in during the reveal that the human had a Vulcan ancestor. (00:14:30)
Factual error: When Capt. Archer joins Travis in a weightless environment he refers to in an earlier episode as the ship's "sweet spot", Travis discusses the bad news he received from The Horizon, his parents' cargo ship, with Capt. Archer, and you see tears rolling down (and off) Travis's face. In a weightless environment the tears would not react in this way. (00:06:20 - 00:07:40)
The Breach - S2-E21
Other mistake: As Archer walks into the sickbay, while the camera pans, you can see a bottle of Crystal Geyser water. I noticed the bottle right away but had to pause it to see the brand. (00:39:00 - 00:40:00)
Other mistake: Two Borg are discovered North of the Arctic Circle. One is covered in ice, the other encased in ice. Carbon dating shows the wreckage to be over 100 years old (to tie it in with Star Trek:First Contact). The Borg are inactive and unable to repair themselves until they are "defrosted". The temperature above the Arctic Circle doesn't usually drop below -100°F. The Borg have been shown to work very well in the vacuum of space which is 3-4K (roughly -454°F). If they can survive that, even being frozen in a solid block of ice would not slow them down. The nanites have to be in their "blood" and operate at the cellular level. That cannot be damaged by re-entry and the crash. [This is one of those entries that keeps being corrected and recorrected - I'll leave it up to people to make up their own minds.]