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)
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.
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)
Answer: The torpedo stopped him from succeeding.
Bowling255 ★