Continuity mistake: In episode Revulsion (Season 4 episode 5), commander Chakotay says that Voyager's astrometrics laboratory hasn't been updated since the ship left space-docks. In later episodes it is stated that Voyager didn't have an astrometrics when it was built. In Shattered (season 7 episode 11), Chakotay time-travels back to the day Voyager leaves for its first mission and tells that times Janeway that they are going to the astrometrics, to which Janeway comments, "Voyager doesn't have an astrometrics".
Continuity mistake: Tuvok and Paris' rank seems to skip around during the first season. Despite being listed in the credits as 'Lieutenant Tuvok', Tuvok starts the show as a Lieutenant Commander, with the signatory three collar pips, one black and two gold. At certain points, however, he is seen with only two gold pips (signifying Senior Grade Lieutenant). After season one he remains a Lt. Commander with no reason for the lack of continuity offered. Similarly, Paris starts the show as a Senior Grade Lieutenant, but sometimes instead of two gold pips he has one gold and one black, the signifier of a Junior Grade Lieutenant. After season one he is always presented as a Junior Grade, excluding his brief demotion to the rank of Ensign in a later series.
Revealing mistake: If you look carefully when Neelix shoots the bins of water causing the water to rush out you can see a faucet opening on one of the bins.
Continuity mistake: The registry on the shuttle that brings Paris to Voyager keeps changing between "NCC 71225" and "NCC 1701-D".
Plot hole: To escape the 'event horizon', a rupture in it is widened to 120 meters (which allows 2 meters clearance on each side of the ship). Soon after, the rupture has shrunk to 110 meters wide, and Janeway decides to 'punch through' anyway. The ship does so with little difficulty, but the whole issue seems pointless since the rupture was far larger 'vertically' than 'horizontally' (relative to the view from the ship), so tipping the ship on its side would have allowed plenty of clearance to slip right through.
Factual error: The event horizon of a quantum singularity (aka black hole) is not a physical barrier you can punch a hole through but a theoretical one, which can't be escaped from without faster then light travel.
Visible crew/equipment: Neelix says to Chakotay 'I don't understand, it's right here,' referring to the dilithium ore. As soon as the camera changes to show him walk into the large cavern, a boom microphone is quickly pulled away from covering his face. (00:07:45)
Continuity mistake: In sickbay, when Kim tells the captain he's analyzed the tricorder, the tricorder is open. In the next shot it's closed.
Emanations - S1-E9
Factual error: To protect the warp core, Janeway instructs Paris to move away from the rings at Warp 7. Moments later (Janeway, Torres and Tuvok are still in the same position), Paris tells Janeway they are 0.6 light years away from the rings. Warp 7 is 656 times the speed of light. It would take about 8 hours to travel 0.6 light years at Warp 7.
Suggested correction: The warp scale, especially since it's fictional, has never been precisely defined.
While it's never been defined, certain aspects of warp speed drive and the length of a light year are accepted. Even if Warp 7 is double what is suggested in the mistake, it would still be 4 hours. The scene in question shows no lengthy travel at Warp 7.
Character mistake: When trying to trap the energy mass they created, B'Elanna announces, "Now it's trapped on three sides," to which Paris replies, "It's changing course. Heading for the open side." Since we function in 3-dimensional space, unless they are trying to trap it in a triangular-based pyramid, the number of "sides" to be concerned with is six.
Revealing mistake: Tuvok is behind a forcefield in Sick Bay, with the Doctor, Kes, and Captain Janeway looking at him. He tries to break the forcefield and is rendered unconscious and thrown to the floor. Janeway and the Doctor rush to pick him up and put him on the bed. Before they start to pick him up, he lifts his head and starts sitting up (to assist them, not because his character is conscious). (00:38:26)
Projections - S2-E3
Other mistake: At the beginning of the episode, as B'Elanna is working her way out through the doors, the Doctor cowers and tries to hide behind things. There is no reason for him to be afraid. He can't be hurt under normal conditions - this proves to be the case later when he feels pain and says he is not programmed to feel pain, and we learned earlier in "Phage" that he can change whether or not things pass through him.
Plot hole: In this episode Kes states that she has to decide now whether to have a child or not because Ocampa women can only get pregnant once and deliver one child. If that was the case they would have died out a long time ago, or never even evolved, as two people only getting one offspring would reduce the population to 50% of the original figure each generation.
Suggested correction: It's also possible that it's simply required of Ocampan women to give birth the first time they go through it, and can then experience it again.
Nothing in the dialogue suggest Ocampa's can have additional children. While we can speculate about fictitious species, it's still a plot hole due to writing. Kes states she's going through the "elogium" which is a time of change where her body prepares for fertilization. She then explicit states the "elogium" only occurs once. While the doctor compares it to puberty, the elogium is both sexual maturity and "heat", that is, the time a female is ready for fertilization.
But it doesn't ever state the normalcy of birthing for Ocompans. Perhaps sextuplets is the norm?
Kes frequently used the word "child." If it was normal to give birth to more than one, she would know this and should say "children."
Do not forget that this is all done through the universal translator. For all you know the Ocompan word for child and children is the same so the translator cannot tell the difference.
Revealing mistake: When Kes is eating the spawn beetles, the same shot is used twice for when she scoops out beetles from the tray. The untouched beetles are all in the same place, and there is a beetle that is nearly flipped by her thumb both times.
Continuity mistake: When Torres and Paris enter engineering, the warp core is dark showing that it is offline. Minutes later, it is illuminated and online. (00:19:15 - 00:28:30)
Parturition - S2-E7
Revealing mistake: On the bridge, as Tuvok monitors and reports on the pursuing ship's weapons, you can see what looks like a wristwatch on his right wrist as he works the controls. (00:35:35)
Character mistake: As Voyager is bombarded by the cyclone, Paris reports that Voyager is at 20,000 meters and falling. 28 seconds later, he reports that Voyager is at 18,000 meters and states that, at this rate, they will crash in 10 minutes. However, if they drop 2000 meters in 28 seconds, they would actually crash in 252 seconds (just over 4 minutes). One might argue that perhaps it was calculated that their descent would slow down as they approached the surface, but later they fall from 2000 meters to 1000 meters in 14 seconds - the same rate.
Resistance - S2-E12
Continuity mistake: When Caylem dies in his close up shot, his head falls to his right shoulder, but in the next shot showing Captain Janeway holding him in her arms, his head is angled to his left (away from the camera).
Dreadnought - S2-E17
Continuity mistake: Dreadnought states there are fifteen priority targets approaching. On radar sixteen Rakosan ships are displayed. Then just before the Dreadnought attacks (and destroys three of) the approaching ships, there are a total of nineteen Rakosan ships displayed on radar.
Continuity mistake: When Samantha is holding her baby while the captain talks to her, her hands are apart with her right hand under the baby. In the next shot, her right hand is on top of her left hand and not under the baby.
