Continuity mistake: In the scene right before the shuttle's crew finds the Romulan ship and the Enterprise, Geordi calls the shuttle craft's cockpit to explain the temporal disturbances. Captain Picard, Troi and Data walk into the shuttle's cockpit room and Troi puts her right arm on Geordi's chair. As Geordi, Data and Captain Picard are talking you can see Troi's wrist hanging off the chair, but when the camera cuts directly in front of Geordi her whole wrist is on the chair. The camera then cuts back and you can see that Troi's wrist is still hanging off the chair.
Continuity mistake: In the scene where Captain Picard reaches for the aged fruit, he screams while holding his right wrist with his left hand. As Troi, Geordi, and Data rush in you can see Captain Picard holding his wrist up in the air. The camera then cuts directly in front of Captain Picard and you can see Troi scanning his wrist but he isn't holding his wrist anymore. The camera then cuts directly in front of Troi and Geordi and you can see that Captain Picard is still holding his wrist. The camera then again cuts back to Captain Picard and he isn't holding his wrist anymore.
Continuity mistake: Picard states that the energy beam appears to come from the deflector array, in later shots it is coming from the rear of the star drive section.
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