Continuity mistake: In the beginning of the episode, Riker, Geordi, Worf, Data, and Pulaski are playing poker. Pulaski puts two neat stacks of chips in the center beside some chips in a pile. It then shows Worf putting similar stacks in the center but Pulaski's stacks are not visible and they should be. Then when Worf wins the hand, the camera is showing a wide shot of him pulling the chips towards him and you can see his and Pulaski's neat stacks of chips.
Continuity mistake: The Bringloidi leader keeps saying that they've spent 300 years building their society, but this episode takes place in 2365, and it's stated that his ship launched in 2123, making it 200 years.
Continuity mistake: Klingons measure distance in kilometers in this episode. However, in all other Trek shows and movies, they measure in kellicams. [This was apparently during a misguided attempt by the Empire to adopt the decimal system (for Galactic consistency), even though the change was wildy unpopular with the public and military alike. While some ships, like in this episode, gave it a good try, the change was short-lived and eventually abandoned. However, until this claim can be backed up by a reference within Star Trek canon, it stands as a mistake.]
The Royale - S2-E12
Continuity mistake: As the Texan follows the dice on Data's last throw, his glasses are on. As he complains about losing his bet, his glasses are suddenly missing.
Continuity mistake: When Data bends the bar, he does so much that the sides are almost parallel with a very acute angle. When Riker puts it on the desk, it's much more curved and the sides aren't as parallel anymore.
Continuity mistake: Wesley says that he's departing shuttle bay 2, but on the floor, it says shuttle bay 3.
Continuity mistake: Looking at the shuttlecraft while sitting in the shuttle bay and after it has departed the Enterprise, you can tell they are different types of shuttles. The one in the shuttle bay has more angular lines with straight edges. The one outside the Enterprise has more curves than angles to its lines.
Continuity mistake: When the original Picard shoots the duplicate Picard with a phaser in the shuttlebay, he shoots him square in the chest. But in later shots, the scorch marks from the phaser are on his abdomen area.
Continuity mistake: When Data is dealing the cards for 7-card stud, they show him dealing 1 card to everyone. In the close up, he's now dealing everyone a 2nd card. When it cuts to his hands however, everyone only has 1 card and he's dealing them a 2nd card again.
The Royale - S2-E12
Continuity mistake: When Data is first playing Blackjack, his first face up card dealt is a 7, followed by a 5. In the close up when the final card is dealt, the first two cards are now 3 and 2.
Continuity mistake: When Data is telling Guinan jokes and is then called to the bridge, he's holding the cigar between his first two fingers. In the next shot, he's holding the cigar between his thumb and first finger.
The Dauphin - S2-E10
Continuity mistake: When Wesley and Salia are on the holodeck looking at Roseau 5, Salia's left arm is around Wesley's back. In the next shot, both her hands are wrapped around his arm.
Continuity mistake: Near the end, when Pulaski finally stops the infection in Riker and is just about to contact Picard with her success, look at Riker lying on the table. His eyes are open, then he closes them slowly. The next scene has Riker opening his eyes for the first time after recovering from the procedure.
Continuity mistake: After Pulaski examines Riker's leg, and readies to beam up, he leans to the right to get up. In the wide shot, he does it again.
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.
Continuity mistake: As Worf goes to enter the portal to the Enterprise carrying Data, his right hand is free, and his left is holding Data's left hand. Appearing on the bridge, Worf's left hand is on Data's leg, his right hand on Data's wrist.
Continuity mistake: When the security man gets tossed by the Borg, as he lands and rolls next to the far wall, his phaser falls out of the holster, and lands next to his shin. A second later, it's about two feet away from his leg.
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