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".
Visible crew/equipment: When Deanna and Riker stop at the turbolift to discuss Data, before the doors open to reveal Data, in the shot facing Deanna the reflection of crew movement is visible on the trim's surface, just over the turbolift.
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