Corrected entry: When we see the now blind Tuvok shaving, he is using a metal blade, the type still used today, and promptly cuts himself with it. However in TNG, Geordi La Forge (also blind, but using a VISOR) is shown using a bladeless razor with a little light beam that wouldn't cut him. One of these should be available on Voyager, over 10 years later. Lack of power can't a problem, as Tuvok had the lights in his room on the whole time, despite not needing them on account of being blind.
Corrected entry: When Chakotay's comet removal simulation erases 8,000 civilizations, Annorax tells him that 4 billion years before, material from the comet was the catalyst for the eventual development of several civilizations. However, comets, by their very nature, are short-lived, around 10,000 years. There is no way a comet that seeded life across multiple solar systems 4 billion years earlier would still exist.
Correction: Not entirely correct. The typical dynamical lifetime of a comet is about 500,000 years, which of course, can vary. After its dynamical lifetime, the comet becomes a dead comet, Once a comet has lost all of its available volatile materials, its coma and tail will disappear and the remaining inert nucleus will take on the appearance of an asteroid. Since it is never mentioned what type of comet they are discussing, the scenario is plausible.
Correction: It has been shown on a number of occasions that some species and cultures prefer to use a blade to shave. Vulcans do so as part of their mental control.