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.
Continuity mistake: When Janeway and Neelix chase after the mysterious figure moving away from the down the dead end corridor, the wall is lit up, and the shadow moves across it showing direction of travel. After a quick cut, the wall they approach, and the corridor is noticeably darkened.
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 ★