Visible crew/equipment: When Picard, Spock, and Data have just escaped from Romulan Commander Sela, when they are walking out of the room look at the green glass ornament - you can see a reflection of a crew member. Corrected on Blu-ray. (00:41:10)
Continuity mistake: When Dr Marr and Data are talking in the cave about her dead son, she is holding the tricorder upside down.
Revealing mistake: In season 5, "The Game," the brainwashed crew members hold Wesley's eyes open to force him to see the mind-controlling game. Their intention is to prevent him from closing his eyes, which would protect him from the device. While they are doing this, he blinks.
Visible crew/equipment: Just before encountering the Lysian destroyer the boom is visible in the top left of the screen very briefly
Continuity mistake: In the scene where Data is brushing Timothy's hair into a copy of his own hairstyle, he stops, kneels down and asks Timothy "Timothy, are you having bad dreams?" In this shot there is a big tuft of hair on the right side of Timothy's head that sticks straight out. When their conversation is over and Data stands up in the wider shot, all of Timothy's hair is in place.
Continuity mistake: When Ro and Picard are among Ro's people and she gives her jacket to a child (saying something like 'this is what I was, once') she never removes her commbadge. However, there's a commbadge neatly placed on her grey tank top - even though she didn't even remove it from the jacket, let alone put it on her shirt.
Continuity mistake: In the very first scene, where Data is shuffling the cards, you can see his silver and gold chips are neatly stacked up straight. The camera then cuts to Commander Riker and then back to Data and his chips are crooked at the top and at the bottom.
Character mistake: When the artifacts from the late 19th century, found in a cave, are identified by the away team, Data identifies the pistol as a "double action" Colt 45, circa 1873. The pistol is a Colt single action army, caliber .45. Certainly not a "double action".
Character mistake: When Commander Riker is assembling his away team to visit the planet's surface, he orders Dr. Crusher to bring a medical team. But when the away team is beamed down, Crusher is the only medical officer there.
Continuity mistake: In Ten Forward, when Deanna and Data are done playing 'chess', the positions of The Game-pieces on the lower board level between them changes repeatedly, depending on camera angle.
Visible crew/equipment: A boom Mic is visible about nine minutes in, just as Riker and Picard begin walking down the corridor talking about Lwaxana Troi getting married aboard the enterprise.
Deliberate mistake: To fix the error of the Enterprise firing phasers from the torpedo bay, the Blu-ray version uses footage from "The Best of Both Worlds" to show phasers firing from the dorsal emitter. In doing so, they created a new goof; the planet El Adrel is not visible in the background during these shots.
Visible crew/equipment: When Dr. Crusher is trying to save the Borg, just before Worf says "lower the force field" a boom mic is visible.
Factual error: When the starboard nacelle causes the ship to spin, the view of the stars on the main screen on the bridge should move toward the right side of the screen, rather than standing still.
Continuity mistake: When the Enterprise activates the deflector dish, there are four points emitting beams. However, there are five beams emitting after the angle changes.
Other mistake: After the signal change to a continuous output, the Crystalline Entity vibrates. As it does, look at the background stars. They also vibrate in time with the Entity, although the signal is focused on Entity alone.
Continuity mistake: When Picard looks down the mountain to look at the town he has a straw hat in his left hand, next shot it's gone.
Answer: He brought the Borg to the Alpha Quadrant and showed them that it was full of worlds waiting to be assimilated. Guinan's homeworld was their first stop, and they assimilated everyone and took over the planet, leaving The Survivors of her race without a home. Q is ultimately responsible for that.
Captain Defenestrator
By the time Q takes the Enterprise to meet the Borg, Guinan already knew who they were and they had already destroyed her world. Therefore the above answer can not be right. I believe Guinan is much more than she appears, and her people have had encounters with the Q in the past. It is these interactions, that obviously were not pleasant, that fuels her distrust.
oldbaldyone
That's what the above answer is saying. Q brought the Borg to the Alpha Quadrant (not Earth) and the Borg destroyed Guinan's home world in the late 2200's, which is why she hates Q. Although she met Q in 2160 and they both saw each other as enemies right away.
Bishop73