Revealing mistake: When Picard looks out the window of the Dixon Hill office he sees the cars passing by each other, the traffic light is right in front of the window as if the entire building is not only in the middle of the street but only one story high.
Visible crew/equipment: When Worf addresses Klingon captain K'Nera, a microphone dips into the shot over Worf's head. (00:33:10)
Visible crew/equipment: In the scene in the cavern where Wesley fires his phaser to heat the rocks to keep him and Picard warm, Wesley's shadow is in the wrong place. The camera is in almost a direct line of sight between where the rocks are (which are supposed to be providing the light source) and Wesley with the cavern wall behind him. After Wesley fires his phaser and the room illuminates, his shadow should be either directly behind him or to the left of him, but his shadow appears to the right side of him. The only way his shadow would be there was if the light source was off camera a good distance to the left.
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.
Nth Degree - S4-E19
Other mistake: After Data reports the bypass blocked, Riker goes to call to Barclay. The chirp preceding the computer, now Barclay's, response occurs almost simultaneously with the call, rather than a second or two gap between the call and chirp.
Continuity mistake: When Picard, Ro and the others arrive at the refugee camp to meet with Keeve Falor, the type of uniform top Ro is wearing has its zipper at the back in the center - with no seam whatsoever at the front. When she kneels down in front of The Child, it has changed to the open-front jacket type, so Ro can touchingly give it to The Child.
Power Play - S5-E15
Continuity mistake: On the planet's surface, when the away team are knocked unconscious their positions on the ground differ significantly between shots.
Where Silence Has Lease - S2-E2
Continuity mistake: When Riker and Worf are beamed off the Yomato, Riker is on the left of Worf. When they materialize, Riker is on Worf's right.
Revealing mistake: The Klingon which challenges Gowron, and which Gowron kills, is seen breathing when he should be stone dead. (00:16:10)
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