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.
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: 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 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. Voayger 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 capitol ships.
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.
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: 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.
Character mistake: At the start, Captain Janeway reveals that she has discovered Tuvok's birthday. Then she says it's not long before he hits the big 3-digits (meaning 100 years old). However, Tuvok was 107 when he infiltrated the Maquis and they've already spent 6 years on Voyager. Even if she didn't discover his birth year and was only guessing. Tuvok would not have replied with "indeed" but pointed out she is wrong.
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.
Plot hole: Tuvok says that he was born on Stardate 38774. But he was born in 2264, when Stardates were only counted in the thousands, not the tens of thousands. If he were really born on SD 38774, that would mean he was born only a few years before the Enterprise-D was launched.