Revealing mistake: In the scene where Barclay reappears on the transporter with the crewmember, they both fall to the ground. The transporter chief had put up a forcefield around the transporter chamber, in case something goes wrong. However, when the crewmember falls to the ground, his foot goes right through where the forcefield is meant to be. It is still active, as only a few seconds later we see it being deactivated.
Revealing mistake: In Amanda's quarters, when she repulses Q, as he flies toward the corner, you can tell it is his stunt double.
Revealing mistake: In the cargo bay, as Riker stands alone, through the whole scene where a case is about to hit him, you can tell it's a stuntman with a bad wig.
Revealing mistake: When Frank Hollander visits Eli in jail, you can see a dummy in the cell.
Revealing mistake: When the first villain hits Worf with the chair, just as Alexander is yelling "look out", you can tell it is a stunt double.
Revealing mistake: When Picard and Cmdr. Daron are in Picard's quarters together for the first time, watch Picard play his Inner Light theme. The hands playing the flute are obviously not his.
Descent (1) - S6-E26
Revealing mistake: In the hand-to-hand with the Borg soldier, Data's stunt double is easily identifiable.
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