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.
Revealing mistake: When Picard takes his seat in the Captain's chair after informing Dathon's crew he has been killed, the reflection of an overhead rig of gelled lights can be seen in the blade of Dathon's knife, which Picard is holding, as Picard says the line, "but at least they're not new enemies."
Revealing mistake: At the end of the episode, when Mrs. Troi enters Ten Forward naked, the flesh-colored top Majel Barrett is wearing is visible.
Revealing mistake: The Klingon which challenges Gowron, and which Gowron kills, is seen breathing when he should be stone dead. (00:16:10)
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