Character mistake: Previous episodes have established this story arc to be occurring in the year 2154. Yet here, when T'Pol records her log, she cites the date as 2152. (00:32:00)
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)
The Catwalk - S2-E12
Continuity mistake: T'Pol says she has never been camping, but she went in "Strange New World."
In a Mirror, Darkly (2) - S4-E19
Continuity mistake: The Avenger attacks the Defiant's saucer section, but later, no damage is visible in this area.
Character mistake: In Engineering, Trip calls Commander Kelby "Lieutenant."
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.
Other mistake: When Captain Hernandez gives an order to her helmsman, she says "lieutenant". But the helmsman has only one pip on her uniform, she's an ensign, not a lieutenant.
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.
Factual error: At the very end of the episode after Loomis is arrested, the camera pans away from the Detroit street, but mountains can be seen in the background on the horizon. There aren't any mountains or even large hills near Detroit.
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)
Visible crew/equipment: In the episode, "Anomaly," at the beginning, when Phlox is looking at his animal cages, you can see a string or wire attached to one of them, presumably the means by which the cages are shaking.
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)
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."
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)
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.]
Revealing mistake: While Archer and the crew discuss the capabilities of The Xindi vortex technology and whether or not to go to Azati Prime, Archer asks Trip to see the data that Trip has collected from the Degra's ship. The camera pans to the display screen, on which a Mac mouse pointer is visible. It is positioned on the line going downward from the red giant.
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.
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)
Continuity mistake: At 38:20, T'Pol (as acting captain) says that they have resumed their course to Azati Prime; however, from 39-42 minutes, Captain Archer and Trip discuss the "current" status - that they are still orbiting the planet and then the Captain orders Trip to tell Travis to set a course for Azati Prime at maximum warp. (00:38:20)
Other mistake: They show the tether and tether anchor fall out of the ship and fall behind, much in the same way as throwing something out of a car. However, it was still in the warp bubble and should have continued to be moving at warp 5 with the ships. We see later Columbia extend its warp bubble around Enterprise and Enterprise remains at warp 5 after cutting their engines. But, if the tether is no longer affected by the warp bubble, it should have been instantaneously out of view.
Suggested correction: Too much supposition, especially regarding fictional technology.
This correction is too vague and gives no counter argument to support the statement. Either it's affected by the Warp Bubble and stays at Warp 5 or it doesn't. Even with the inconsistency of warp speed, the ship is still traveling 20-30 million miles a second (23.2 million miles a second at standard speed). An object that small would be out of sight within a mile or less (fictional technology or not). Since we know the object isn't traveling at Warp 5 (otherwise it wouldn't fall behind as it did), it would have to be traveling at least Warp 4.99999999 to stay in range as long as it did (a speed never established in-universe). It's also been established in-universe when a ship comes out of warp, it has no inertia so it will not continue to drift. Given in-universe established facts about the fictional technology, there's nothing to support the idea the object is still traveling at Warp 4.99999999 (at Warp 4.9999999 the object would still be out of sight after less than a second).