New this month Other mistake: 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.
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.