Revealing mistake: As Seven starts to explore, there's a flashlight floating next to her. There's no atmosphere, therefore no breeze, but it's slightly moving before she touches it.
Revealing mistake: If you look closely at the hot air balloon, in the shot before the message is attached to it, you can just see a wire holding it up.
Revealing mistake: As Icheb's parents turn their faces towards the sun to look at Icheb, the edges of the prosthetics used for the ridges on their noses are visible.
Revealing mistake: Right at 40:30, if you look in the top left corner of the LCD screen, you can see a mouse cursor. Six seconds later it starts to move around. It seems like someone noticed and tried to move it out of the scene. (00:40:30)
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 ★