Other mistake: When Scotty goes to the holodeck to visit the original Enterprise, the computer tells him there are 5 Federation vessels with that name. (NX-01 served before the founding of the Federation so this is technically correct.) Scotty specifies NCC-1701, "no A, B, C or D." The computer then tells him the program is ready. The computer should have asked him if he wanted pre or post refit NCC-1701. The ship we see in the Original Series was rebuilt/refit into the ship we see in The Motion Picture.
Revealing mistake: At the end of the episode, when Mrs. Troi enters Ten Forward naked, the flesh-colored top Majel Barrett is wearing is visible.
Other mistake: While down in the pit Geordi makes a couple of spikes to climb out with. When the phaser beam is melting the ore, the metal goes molten about two inches in front of the beam. Also, the spikes are rounded, like handles. The molds he made would have left a flat side.
Other mistake: One of the physical appearances Lal considers adopting is an Andorian female with green skin. In the Trek universe, Andorians invariably have blue skin (the Aenar are a variant of the Andorian race but are depicted with bluish-white skin, still not green). And while other humanoid races have been portrayed with different skin tones, there are some races that have only one skin hue. (ie, Andorians are always blue, Orions are always green, Ferengi are always light orange.) It is highly unlikely she or Data designed it with different skin as Data wants her to fit in, and Troi makes no mention of it.
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.
Conspiracy - S1-E25
Other mistake: When Riker is knocked into the glass table, he should have been bleeding from the impact, but when the close up shows him unconscious, he is not.
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.
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