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)
Suggested correction: There is nothing incorrect about what he said. They will start ageing hundreds of times faster than in normal space.
Aging implies getting/feeling older. They'd only be "aging" relative to normal space. What would happen would be more akin to time travel, with the universe getting older around them.
But the point is, they wouldn't age faster just because "normal" time slows down. If they spent a year on the planet, they'd age 1 year, not 100 years.
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.
Visible crew/equipment: Neelix says to Chakotay 'I don't understand, it's right here,' referring to the dilithium ore. As soon as the camera changes to show him walk into the large cavern, a boom microphone is quickly pulled away from covering his face. (00:07:45)
Continuity mistake: After Starling is beamed out of the limo, Rayne opens the door and escapes. The door is still standing open when the chauffeur starts the car. But in the reverse angle as he drives away, the door has closed itself. (00:20:10)
Continuity mistake: When Tom explains to Alice why he can't leave the Voyager, he has a three-day beard. Later in the ship, when Alice convinces him to turn on the neurological interface, he is cleanly shaved. But in the next scene he has his beard back again.
Revealing mistake: When Tom is reading the Klingon romance novel, he presses the button to turn the page, yet the text is always the same.
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.
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.
Visible crew/equipment: Approximately nine minutes into this episode, as Tuvok approaches the crazed Hirogen, two stage crew members can be seen at the top left of the screen. The first is a rather plump man wearing what appear to be blue jeans, and a polo shirt, while the second is squatting down in front of the first wearing shorts and white sneakers.
Continuity mistake: Paris reports that several ships have dropped out of warp off of Voyager's port bow, but when the ships are put on screen, they are approaching from starboard aft.
Basics (2) - S3-E1
Plot hole: Paris asks the Doctor to disable the phaser banks. How can the Doctor, who can't exit from sick bay, disable banks in engineering? And if it is possible to disable them from sick bay, why did Suder go to engineering?
Continuity mistake: Early in the episode, the Kyrian historical researcher plays a simulation of events aboard Voyager that include Janeway killing a Kyrian and then throwing the rifle to a crewman. Later, he replays the simulation for the Doctor, but subtle details of this 'same simulation' change, most notably the way the female crewman raises her rifle much sooner the first time we see Janeway walk past her, and the difference in the way the male crewman catches Janeway's rifle. (00:14:15 - 00:26:20)
Other mistake: When Seven talks to Lt. Com. Tuvok when he is shaving, she refers to him as "Lieutenant," rather than "Commander." Starfleet follows American naval doctrine with respect to rank structure and military courtesy - Lieutenant is not an acceptable abbreviation of Lieutenant Commander, and with the Borg having assimilated Starfleet vessels and individuals in the past, she'd know their rank structures.
Other mistake: In this episode Voyager sends the doctor to a federation ship in the alpha quadrant through a transmission using an alien communication network. Right before he is sent you see him in the astrometrics lab and he steps up on a platform wearing his mobile emitter. His program is then sent through the data stream and the mobile emitter is sent with him. Then when he arrives it is not there. Firstly, the mobile emitter can't be sent this way, only the doctor's program can. It can be beamed but that was not the case here. Secondly, in other episodes where the doctor is taken offline while wearing the emitter they show it drop to the ground. They don't do that here as it appears to dematerialize with him. (00:07:00 - 00:08:00)
Revealing mistake: When Paris and Rayne are driving through the Los Angeles suburbs in her van, they never change their direction of travel, but they pass the same sequence of houses twice. (00:31:05)
Visible crew/equipment: When the former Borg drones are awakened in sickbay, there's a pinkish T-mark visible on the floor behind Seven, at the bottom left corner of the screen. (00:19:10)
Other mistake: When Janeway plays the message from the Admiral, she tells the computer to advance to time index 121.4. each 0.1 of the time index equals 1 second. We hear the message play for 4-5 seconds, but when the video is shown, the time index is only 121.5.
Continuity mistake: When future Kes is talking to Neelix in the kitchen, when he says he's already reserved the holodeck, he's holding the smaller container. In the next shot, the smaller container is on the counter and he's holding the bigger pot.
Character mistake: When the now human Borg children are sculpting, one of the children tell Seven he made a cube that's precisely 1/1,000 the size of a Borg vessel. Borg Cubes are described as 3 kilometers in length, if not bigger. 1/1,000 of that would be more than 9.8 feet in length. 1/10,000 the size would have been a more accurate description.
Continuity mistake: When Seven and Naomi are playing Kadis-Kot, the pieces on the board and on the table change after Seven wins in the next shot.