Continuity mistake: As Janeway calls the bridge after a conduit is blown out by Kes, her combadge is askew. A moment later when they meet Tuvok, it's correct.
Mortal Coil - S4-E12
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.
Continuity mistake: The array surrounding the micro-singularity is shown collapsing twice, once when weapons fire causes Voyager to lose control over the anti-thoron radiation it is emitting and again when Voyager is attempting to beam Seven of Nine and Tuvok off the Hirogen ship.
Continuity mistake: When Seven gives her log entry at the beginning of the episode, she lists the Star Date as 15781.2. This is a misstatement of the correct star date, 51781.2.
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)
Chosen answer: Before Q sent the Enterprise to the beta quadrant to officially contact the Borg, there were already indications that the Borg was beginning to reach Federation territory. There were remarks towards the end of the first season of the Next Generation that several of the furthest Federation outposts were being attacked by some unknown enemy. They suspected the Romulans, but when contact with the Romulans was re-established, they learned that it was not them. The Hansens had simply figured things out much earlier than anyone else in the Federation. They learned about the Borg nine years earlier, but Starfleet mainly took notice when their outposts started getting wiped out. It is logical to assume that there were indications of Borg scouting parties and research efforts well before that.
Garlonuss ★