Imperfection - S7-E2
Continuity mistake: Tom Paris is already wearing his wedding ring in the scene where he is assisting the Doctor with Sevens operation. He doesn't get married until the next episode.
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.
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)
Continuity mistake: The Doctor incapacitates B'Elanna to prevent her from fixing his subroutines. While unconscious, he looks at her from afar with evil intent. When he looks at her from a distance, her arms are along her sides. After the commercial break when he comes up to wake her, her hands are folded across her chest. (00:25:40)
Revealing mistake: Tuvok is behind a forcefield in Sick Bay, with the Doctor, Kes, and Captain Janeway looking at him. He tries to break the forcefield and is rendered unconscious and thrown to the floor. Janeway and the Doctor rush to pick him up and put him on the bed. Before they start to pick him up, he lifts his head and starts sitting up (to assist them, not because his character is conscious). (00:38:26)
Other mistake: They show Kes as a baby but her ears are human. (00:42:25)
Basics (2) - S3-E1
Deliberate mistake: After Voyager's secondary phaser banks overload, everyone on the ship seems to be severely injured, but Seska's baby is perfectly fine. This is likely to be a conscious decision by the writers. (00:40:30)