If a piece of a brown dwarf star even a quarter the size of the one that hit the moon in this movie actually hit the moon, it would punch right through it and keep on going, especially at the oblique angle of the impact.
A brown dwarf is not a star. It is more like a gas giant like Jupiter but larger. It does not have the mass to begin fusion. The closest thing to the stellar object in the movie would probably be a neutron star. That is if a neutron star were to somehow break apart or if a piece was ejected during its formation.
The elliptic orbit of the moon is depicted and described as an ellipse with the Earth in the center. In this way, the moon would be closest to the Earth twice per orbit. In reality, the Earth should be in one of the two focus points of the ellipse so that the moon is closest on one point, and most far away on the opposite side.
General Vaughn has his branch of service on his uniform lapel. Generals do not wear this type of insignia on their uniform.
Astronaut is Russian, however he is seen with Netherlands flag instead of the Russian flag.
There are several scenes, particularly at the start of the movie that ignore the fact that the world has multiple time zones. It's not night everywhere.
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