Continuity mistake: In the opening sequence, the ship is positioned so that Shuttle Bay Two is aimed at the phenomena. But a moment later, the ship is facing into the stellar material.
Other mistake: As Guinan sits at the desk, she reaches toward, but doesn't touch, the control for the screen, but it activates.
Continuity mistake: As the ship fires the torpedoes, the familiar registry number on the underside of the saucer is completely missing.
Continuity mistake: Near the end of the episode, as they are preparing to beam down to the planet, Riker tells Warf to set his phaser on stun. He then holsters his own phaser and the transporter is activated. However, when they materialize on the planet, Riker is holding his phaser in his left hand.
Bloodlines - S7-E22
Visible crew/equipment: When Picard and his Jason have their "father and son" chat in the caves, you can see the mike shadow moving up and down a few times on Jason's leg. (00:33:20)
Other mistake: As Crusher enters the police station, Data says "Hiya, Doc. What's cookin?" He's supposed to be incapable of using contractions.
Revealing mistake: As Data looks at the information on Dixon Hill, as the computer flash feeds, you can see that it's all the same block of information starting with the title of the first novel, which is the title of the episode, "The Big Goodbye."
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: As the Enterprise comes into the frame approaching the cloud, the registry numbers are reversed.
Where No One Has Gone Before - S1-E6
Other mistake: As the Enterprise comes out of warp in galaxy M33, the conference lounge is visible and is a re-use of the opening sequence. The movements of the people is identical.
Encounter at Farpoint (1) - S1-E1
Continuity mistake: As Riker looks at the wooded scene on the holodeck, the water is flat calm, but when the camera looks at him, the water is noticeably more agitated before he gets to the rocks.
Encounter at Farpoint (1) - S1-E1
Visible crew/equipment: As Zorn leans over his desk after Riker leaves, the studio light is reflected on the monitor screen to his left.
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.
Continuity mistake: As Geordi talks to Ms. Rogers, Riker is walking in the background by some containers and a crewman in blue. After a cut to Ms. Rogers, Riker is suddenly alone with a data pad.
Descent (1) - S6-E26
Revealing mistake: In the hand-to-hand with the Borg soldier, Data's stunt double is easily identifiable.
Audio problem: We hear Reva's female member of his choir say "I have been expecting you", but her mouth doesn't move.
Continuity mistake: As Q approaches Picard and Riker's position while playing a trumpet, both of Q's hands are on the horn. A second later, his left hand is down by his side. Then, after he makes cigars appear in Picard and Riker's mouths, his left hand is extended as he says the first part of his lines. A second later, both hands are on his horn.
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