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.
Continuity mistake: As Starling prepares to launch the timeship from the bay behind his office, there is a shot of the exterior of the ship. In the background of this shot, there is a white wall on the right. This wall carries the company name and logo. However the name is misspelled here as Chronowerks, instead of Chronowerx as was shown on the outside of the building and behind Starling and Janeway when they were in the office.
Character mistake: Neelix says that the Great Wall of China, prior to the 22nd century, was the only man-made object visible to the naked eye from orbit. This statement has been long-since debunked, but it's not unreasonable to think the myth perpetuated itself in the future. Still wrong though.
Character mistake: Captain Janeway states the temporal differential ratio is .4744 seconds per minute (meaning for every minute on the surface, only .4744 seconds pass on Voyager). Tuvok calculates that 30 minutes on Voyager would be 2 days 11 hours and 47 seconds. However, at that ratio, 30 minutes would be 2 days 15 hours 14 minutes and 15.9 seconds. Later Tom (who was on the surface) says the last two months for them was only 2 days for B'Elanna (who was on Voyager). But with the temporal differential, 2 months on the surface would be less than 12 hours on Voyager. 2 days on Voyager would be almost 253 days (almost 8.5 months) on the surface.
Plot hole: The Voyager was continuously attacked by small Kazon attack ships. Yet the Captain never orders to increase the warp speed to evade them (In previous episodes we saw that the Voyager has much higher max speed than any ship in the Kazon arsenal). They simply travel at a lousy Warp 2 and wait to be attacked. It would make sense to travel slowly if they were trying to avoid being detected by Kazon but that was not the case. They were attacked constantly. Voyager may be more maneuverable at slower speeds but if you can outrun your pursuers there is no need to maneuver to avoid them. Also, if Voyager was traveling at a higher Warp Speed, there would be no way for the Kazon to array fighter craft ahead of Voyager as they would not be able to overtake Voyager. If they could, there would be no reason to deploy the fighter ships, they could simply engage with their capital ships.
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.
Plot hole: It's stated that only objects or people infused with the chronoton serum can pass through the time barriers, which is why the equipment belts and hyposprays had to be specially modified (these wouldn't be needed if the chronotons were producing a protective field wider than the infused object). But some un-infused artificial objects, such as clothing and com-badges, can pass through them without vanishing. This is most obviously seen in the scene when Chakotay pulls the captain through the barrier, since he doesn't even wait long enough for the serum to spread throughout her entire body, yet alone to perspire into her uniform.
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.
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.
Other mistake: The Doctor scrubs his hands before an operation. He should not have to do this. He is a hologram. He could just dematerialize himself and be rematerialized if he's concerned about contamination.
Plot hole: The atmosphere of the Class Y "Demon" planet is repeatedly said to be highly corrosive and unable to support life. It isn't even safe for Voyager to stay in orbit for very long and Paris and Kim's spacesuits begin to fail after a while of being on planet. However, their shuttle, having been landed on the planet for several hours by the time Chakotay and Seven find it, shows no sign of damage. Even the leather upholstery of the seats or carpet interior (the rear hatch having been left open) isn't dirty. If Starfleet has built its starships and spacesuits out of that same upholstery, this mission would have been no problem.