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.
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.
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: 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.
Factual error: Chakotay says "if our orbit starts to decay, Voyager will begin to feel the effects of the differential, and we'll begin aging hundreds of times faster than we would in normal space". Whilst it is true that they would be aging faster relative to normal space, they would not instantly become old. Time would simply slow around them, so whilst they would be aging faster relative to normal space, they would not all of a sudden become really old - which is how it is made out to be. They would all age the same amount whether in a standard orbit or in a more decayed orbit. (00:06:37)
Character mistake: Captain Janeway's main goal in this episode is to proceed to the holodeck and shut down the lightning shield protecting Chaotica's death ray so Lt. Paris can shoot it with his destructo beam. Throughout the scene where Lt. Paris further briefs Capt. Janeway on her way to the holodeck, the plot is such that her goal is to shut down the death ray, not the lightning shield. (00:26:20)