Plot hole: The atmosphere of the Class Y "Demon" planet is repeatedly said to be highly corrosive and unable to support life. It isn't even safe for Voyager to stay in orbit for very long and Paris and Kim's spacesuits begin to fail after a while of being on planet. However, their shuttle, having been landed on the planet for several hours by the time Chakotay and Seven find it, shows no sign of damage. Even the leather upholstery of the seats or carpet interior (the rear hatch having been left open) isn't dirty. If Starfleet has built its starships and spacesuits out of that same upholstery, this mission would have been no problem.
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.
Character mistake: Species 8472 was trapped on deck 11, behind a force field. When the ship comes under attack by Hirogen, Seven is instructed to get down to deck 11 with a supply of nanoprobes. In the meantime the Hirogen hunter escapes from Sickbay (deck 5) and soon faces off Seven and attacks 8472. When Seven beams them off the ship, Harry says that 'someone has tapped into transporter control on deck 5'. (00:39:00)
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)
Continuity mistake: The shuttle is "parked" in the nebula to get a protomatter sample, and the nebula is visible in all windows. After the shuttle is hit, the camera looks at Tom, and the view in the window is the black of space with stars, rather than the bright nebula.