Continuity mistake: Wesley says that he's departing shuttle bay 2, but on the floor, it says shuttle bay 3.
Other mistake: After the report that Picard is close to death, the scene shifts to a close up of La Forge's hand turning on controls. If you look closely, you can see that both panels are re-purposed CANX-23429 remote control units. The markings are for volume, radio, transmitter, receiver, phone jacks and a microphone jack.
Visible crew/equipment: In the Medical center, as the camera pulls back from Picard, who is lying on the bio bed, the camera is reflected on the panels angled toward the camera.
Other mistake: When the Pakleds shoot La Forge the second time, he raises his arms a bit, seemingly in preparation to go backwards.
Continuity mistake: As La Forge prepares to transport the Pakled shoots him. He reacts, and a second later reacts again.
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