Visible crew/equipment: During Data's second dream experience he imagines becoming a bird and flies through the Enterprise and beyond. As he flies past his father Soong standing at the anvil, a crew member is sitting on the floor by the double doors behind him. This has been edited out in some versions. (00:36:10)
Visible crew/equipment: You can see the boom mic above Picards head when he is in his quarters. (00:11:30)
Visible crew/equipment: In the scene where Geordi and the Captain are in engineering trying to close the subspace hole, you can see a silhouette of the camera in the reflection of the warp core blue lights in the window between the warp core and the console they are working from.
Visible crew/equipment: In the scene where Picard comes to engineering to ask Laforge if he has been successful in locating Riker's homing beacon, you can see the blue light of the warp core reflected in the window. Outlined in that reflection, near Geordi's chest, you can see a studio spotlight.
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