During one of the first attacks, Chakotay checks on an injured crew member and says that she is dead. Moments later when Captain Janeway asks for a damage report, Tuvok states that there are fifteen injured but does not report any crew dead. Tuvok is very thorough and would have included the dead crew member on the bridge in an official damage report.
According to the onscreen text, the event of the temporal weapon ship eradicating the Garenor home world and Voyager avoiding the time change with their new temporal shielding happens on day 65. Both Ensign Kim and the Krenim officer state that they are twenty light years away from each other. On day 70, when Janeway and Seven of Nine analyze the changes in the region in the astrometrics lab, the temporal weapon ship arrives and starts trying to erase Voyager from the timeline. Seven scans the weapon ship and determines that its mass prevents them from exceeding warp 6, allowing Voyager the ability to escape. According to the rescaling of the warp factors that was made prior to Star Trek: The Next Generation (1987), warp 6 should only be about 400 times the speed of light. That would allow a ship to travel approximately one light year every 24 hours. It should have taken the Krenim ship about twenty days to reach Voyager, not five. Voyager could not have been traveling toward the weapon ship since Seven confirms again in astrometrics that they are still twenty light years from where the temporal incursion originated. Discontinuities between warp speed and time are common in the Star Trek universe.
Chakotay and Paris beam up while the temporal shields were active. That's a matter of debate on its own. Moments later the time-ship tried to erase Voyager from time. The exact reason of beaming up Chakotay and Paris is not made clear, in fact that action would have done more harm to the alteration of time.
The Krenim's ship is said to have its aft shielding failing. Voyager takes advantage of this by dropping torpedoes from their tubes like mines, striking and destroying the Krenim ship. The torpedoes are shown striking the forward end of the Krenim ship. The aft section is the rear.
When Seven of Nine says that due to the vessels mass they cannot exceed warp 6, that would mean that there's gravity and air resistance acting on the vessel. Since they're in space and there's no gravity or air resistance the mass of both of their ships wouldn't play any part on either of their engines performance. Therefore it is an inaccurate statement.
Tuvok, who is now blind, and Seven are having a conversation as he was shaving. At one point, Tuvok moves his eyes toward Seven as a sighted person would do. However, when a person loses their sight, other senses become heightened. When he hears Seven speak, his eyes would be able to look in her direction based on the sound of her voice.
When Captain Janeway and Commander Chakotay are in the Astrometrics lab for the first time with the crew. Lieutenant Torres says "That region of space we're about to enter. It looks like it has a lot of M-Class planets." Since Seven of Nine had the entire galaxy displayed onscreen she couldn't have seen each one of the planets, let alone what type of planets they are.
The photon torpedoes that are dropped from Voyager's aft bays are scaled far too large. A photon torpedo is roughly the same length as a human body's height, yet the torpedoes shown would be several decks tall if stood on end.
When Kim and Torres are trapped in a turbolift, the establishing shot shows the top of the turbolift from inside of the turboshaft. This is a re-use of a shot from Disaster (1991), as the turbolift doors are orange. Voyager's doors are black/silver.
After erasing the Garenor civilization from history, Obrist reports that the Krenim Imperium has reverted to a pre-warp state. If that were true, the Krenim warship Voyager had been dealing with at that time should have vanished completely, not just diminished in size, unless the Krenim in that timeline are so bold as to venture into deep space in primitive vessels without warp drive to confront other, more powerful ships, which seems unlikely.
In Before and After (1997), the time-jumping Kes warns Janeway and the crew about a forthcoming encounter with the Krenim Imperium, and the powerful weapons they have. Janeway acknowledges this and determines they will avoid conflict with the Krenim when the time comes; however, when Voyager finally reaches Krenim space, Janeway and the crew act as if Kes's warning was never even made.
Emergency escape pods are designed for use only in an emergency. They do not have warp drive so they could never reach another star in less than a few decades. They have limited propulsion and extremely limited food, water, and oxygen supply. At best they could keep their crew alive would be for days or perhaps a few months. The plan to use them to fly toward the Alpha Quadrant is actually worse than staying on Voyager.
In season 3's "Before and After," a version of the events of this story are portrayed as happening on the same stardate on which the "Year of Hell" begins. The events of "Before and After" take place in a timeline in which Kes never left Voyager, and thus never used her mental powers to push Voyager 10000 light years closer to the Alpha Quadrant, yet somehow Voyager encountered the same enemy at the same time, 10000 light years apart, in both versions of events.
No explanation is offered as to why Voyager can't go around Krenim space. In fact, at the end of part 2, once time has been reset, Janeway receives a warning that the territory is in dispute and gladly orders Paris to plot a course around Krenim space. Had she done that in the first place, the year of hell could have been avoided altogether.
Janeway says that she is "no authority on time travel [...] but this sounds to [her] like a causality paradox." She is correct in her assertion that she is no authority on time travel, as the information she has in no way resembles a causality paradox. A causality paradox occurs when a time traveler creates changes to history that affect their reason for traveling in time in the first place (for example, you go back in time and kill Hitler, but in doing so, you erase Hitler from history, and therefore you never went back in time to kill Hitler, but because you never went back in time to kill Hitler, Hitler rose to power, and because Hitler rose to power, you went back in time to kill him, ad infinitum). There is no paradox involved at all in the situation Janeway and Seven of Nine are observing, history is simply being changed around them.
In his inaugural address, the Doctor says that he was first activated on stardate 48315; however, previous on the series, his activation date has been established to be on 48308, most notably Projections (1995).
Janeway asserts that Voyager is 65000 light years from home. They started the series 75000 light years from home and Kes pushed them 10000 light years closer when she left. 75000 minus 10000 would be 65000, but that neglects the distance Voyager covered on its own over the course of more than three years.
Tom Paris makes an incorrect statement when discussing the steamship Titanic with Captain Janeway and Chakotay. He tells them that the Titanic's transverse bulkhead design would allow the Titanic to stay afloat even if "half the ship" was full of water. Not true. The Titanic was designed to stay afloat with any two of its sixteen watertight compartments (separated by the aforementioned bulkheads) fully flooded, or even the first four forward compartments fully flooded (the Titanic sank because at least five of the forward compartments were opened to the sea). Obviously, "half the ship" represents much more area than five watertight compartments, so Tom Paris' statement is way off.
Seven of Nine addresses Tuvok as "Lieutenant," even though he is a lieutenant commander and the correct shortened form is "Commander."