Pathfinder - S6-E10
Deliberate mistake: When Barkley goes to see Admiral Paris at Starfleet Command, as Nicole tells the Admiral that Barkley won't go away, there's a photo of the Admiral's son, Tom, on the desk. Tom's Starfleet combadge is at his uniform's right side (it should be on his left). But during the conversation there's a closeup of this photo, and Tom's combadge is now at his left side. This is not a flipped shot. The combadge position in the photo was not edited in the 1st shot, though it was corrected in the 2nd shot. (00:24:00)
Deliberate mistake: When the Doctor begins to "fade" in the transporter room his mobile emitter fades with him. Since it's made of solid matter and is not a hologram, this shouldn't be possible.
Basics (2) - S3-E1
Deliberate mistake: After Voyager's secondary phaser banks overload, everyone on the ship seems to be severely injured, but Seska's baby is perfectly fine. This is likely to be a conscious decision by the writers. (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 ★