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. (01:20:35)
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. (01:01:45)
Audio problem: Counsellor Troi visits Picard in his quarters after he finds out that his brother dies. Listen to Picard say "Counsellor - er". There is an audio editing mistake of some sort where you could clearly hear that his voice was dubbed over the original, the original being off by a fraction of a second. The "er" sound from "Counsellor" is repeated. (00:38:20)
Continuity mistake: When the crew of the Enterprise - D is in the Holodeck after Picard has left, Riker is telling Geordi to set royals at stunsail at which time Geordie is looking through a telescope with his right eye. In the next shot when he questions Riker, he takes the telescope down from his left eye. (00:24:05)
Continuity mistake: When Kirk and Soran are fighting on top of the launching structure, Soran falls down the side of the cliff but stops his fall by grabbing a rope hanging from the structure. A moment later the rope loosens and Soran drops fifty feet or so before the rope pulls taught and he stops again. But despite having just dropped fifty feet, he is back at the same place on the cliff before the rope loosened the first time. (01:42:40)
Visible crew/equipment: On the Enterprise-D bridge, when the ship is hit and crewmen go flying, you can see one man go over the bridge railing backward. Twice, from different angles. When he lands the second time, the edge of a blue pad to cushion his fall pops up into the bottom of the shot. (00:16:05)
Factual error: A bottle of champagne in space rotates around its centre of mass, not the midpoint of its axis of symmetry.
Revealing mistake: Roads are visible in the background during the climatic fight sequence on Veridia III, even though the planet is uninhabited. (01:40:35)
Factual error: According to the laws of physics, a massive point source should exert the same amount of gravity on an object X distance away as a spherical object of constant density with radius less than X. It is stated in the movie that Soren's weapon uses "Trilithium," a substance described as a "Nuclear Inhibitor." Stars generate energy and light by way of Nuclear Fusion. That fusion is possible because the intense gravity causes the gasses in a star to compress and heat up. This is essentially fusion by friction. If Trilithium stops the fusion from occurring, all that would be left is a very large body of hydrogen and helium - That is to say, an oversized Brown Dwarf. It shouldn't have been able to alter the gravitational pull of anything since gravity is a function of mass and all the star's mass is still there.