Other mistake: The Doctor scrubs his hands before an operation. He should not have to do this. He is a hologram. He could just dematerialize himself and be rematerialized if he's concerned about contamination.
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: When Neelix and the Captain are following the unknown creature, it turns down a hallway and Neelix says it just ran into a dead end. The two follow and enter the transporter room on their right. However, when they exit the room, they turn to their right again, which should lead to a dead end. They needed to go to their left to go back to where they came from.
Other mistake: At the beginning of the episode, as B'Elanna is working her way out through the doors, the Doctor cowers and tries to hide behind things. There is no reason for him to be afraid. He can't be hurt under normal conditions - this proves to be the case later when he feels pain and says he is not programmed to feel pain, and we learned earlier in "Phage" that he can change whether or not things pass through him.
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)
Other mistake: As Captain Janeway enters engineering after her sonic shower incident you hear crew members calling out problems on the ship. One mentions something about Deck C and another mentions a problem on Deck 22. Letters are not used to designate decks and there are only 15 decks on Voyager. (00:06:30)
Other mistake: In the 3D cinema scenes in the Holodeck, Tom Paris and B'Elanna Torres can be seen using blue/cyan anaglyph glasses and the movie screen can be seen to be in blue/cyan also. This is fine and to be expected. However the shot in which the projection room can be seen behind the couple show the projection is through magenta/green filters. (00:03:30)