Encounter at Farpoint (1) - S1-E1
Revealing mistake: When Q freezes Torres on the bridge, it is easy to tell that directional hoses were used for the effect. (00:06:25)
Revealing mistake: When Data sits in his post, his neck pips are black and then gold. In the next jump scene when he is in the back of the bridge with his commanders, the pips are reversed.
Revealing mistake: As Data looks at the information on Dixon Hill, as the computer flash feeds, you can see that it's all the same block of information starting with the title of the first novel, which is the title of the episode, "The Big Goodbye."
Revealing mistake: When Picard looks out the window of the Dixon Hill office he sees the cars passing by each other, the traffic light is right in front of the window as if the entire building is not only in the middle of the street but only one story high.
Revealing mistake: In the corridor, as Wesley faces the Zaldan, the hallway behind the scene is obviously a painting due to the shadow of the support on the edges.
The Arsenal of Freedom - S1-E21
Revealing mistake: As Data ducks to avoid the blast from the probe, the scene shifts to a wide shot. After Data tosses Yar to safety, he jumps after her. As he does, you can tell it's a stunt man with a bad wig.
Revealing mistake: As Riker is being dragged toward Armus, the wire pulling him can be seen disturbing the sand and the surface of the slime pool.
Conspiracy - S1-E25
Revealing mistake: As Riker swings on Quinn, and a moment later, tossed onto a glass table, both times it can be seen that it's Riker's stunt double.
Conspiracy - S1-E25
Revealing mistake: After the fight with Riker, Quinn throws Worf through the room, hitting a wall. The replicator part of the wall moves.
Revealing mistake: In the sickbay, the wall where the biobeds are located can be easily seen as a wall used for what would be in the Conference lounge. The alcoves have a fabric covering the windows, and it appeared to be a hastily done redress.
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