Deliberate mistake: After the trilithium missile hits the sun, it is shown going out in real time from Veridian III. As the planet is relatively earth-like, it is several light-minutes away from the sun. The filmmakers wanted it to be obvious that the missile was successful, so they ignored the speed of light.
Other mistake: When Capt. Picard is talking about a prisoner transfer, he says he will beam over to the Klingon Ship, then they can beam him down to the planet. He beams off the ship, and is then on the planet, but his transporter pattern (which should be Klingon red) is blue, the Starfleet pattern colour. He must have gone to the Klingon ship first, as his communicator is on his chest when he leaves the Enterprise, but gone when he lands on the planet, meaning someone, obviously the Klingons, took it off him. And don't say the Klingons gave the Enterprise the co-ordinates for Dr Soran's missile site, they're cleverer than that.
Trivia: At the end of the film when the Enterprise crew are being rescued from the surface of the planet where they crashed, Picard is transported from the surface by the USS Farragut. This is also the name of the first ship on which Kirk served as a Lieutenant (mentioned in the original series episode 47 Obsession).
Trivia: The original ending for Generations involved Soren shooting Kirk in the back and Picard finding the body, so he did technically die alone, but the test audiences hated seeing the heroic James Kirk bite it in the back, so all three actors were called in to reshoot the ending, making Kirk's death more purposeful.