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.
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: 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: 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: Gunfire damages the holodeck controls, and the computer announces that safety protocols are now offline. This implies that they were online before the gunfire. If they were still online before the gunfire, the bullets would not have damaged the controls.
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.
Plot hole: When orbiting the planet, Seven says that for every second on Voyager, nearly a day passes on the planet and later Janeway says 3 seconds is nearly 2 days. However, throughout the episode, time seems to move much faster on the planet to fit the plot. It would take more than 6 days for 1,000 years to pass. And in a few hours (3) less than 20 years would pass (hardly enough time for the rise and fall of a civilization). For example, when they receive the transmission, they slow it down and immediately start playing it. The next scene the senior officers are listening to it and the Doctor says nearly a century has passed, but there's no reason (or indication) that they waited almost 15 hours to listen to it.
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.