Factual error: A bottle of champagne in space rotates around its centre of mass, not the midpoint of its axis of symmetry.
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.
Factual error: For the shock wave from the Veridian star to engulf Veridian III so quickly it would have reached the remains of the Enterprise-D (and survivors) so fast they would have no time to think about running.
Factual error: When the champagne bottle hits the ship, the liquid droplets change directions and drip off the ship, despite the ship being in a zero-gravity environment.