Character mistake: B'Elanna replicates and assembles a television from 1956, including a remote control. Tom however says they didn't have remote controls in the 50's. The first wireless remote was invented in 1955 and the "Zenith Space Command" (a remote looking similar to the one in use) came out in 1956, which fits the timeline. Tom is vastly aware of 1950's technology (he seems to know when the television remote came out) and wouldn't make that mistake or B'Elanna would have corrected him given how much research she had to do to set the whole thing up.
Continuity mistake: When Harry uses the scanning tool, the lights alternate between flashing from top down to bottom up and back between angles.
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 ★