Factual error: The Moon is pushed into a "more elliptical" orbit. When the orbit it shown, it is more eccentric than the Moon's real orbit. However, it is centered directly on the Earth. This violates Kepler's first law of motion, which states that a natural satellite has the primary body at one focus of an elliptical orbit. In other words, the Moon should come much closer to the Earth at one end of the ellipse, and recede very far from it at the other end, rather than receding to the same distance in both directions.
Factual error: The Moon is struck by a "brown dwarf fragment" having twice the mass of the Earth, which isn't noticed by anyone on Earth until a few minutes before impact. But an object of this mass would have profound effects on Earth's tides; its effects would have been equal to those of the Moon from the time that the object was within 2 million km of the Earth, over five times the Earth-Moon distance. (At astronomical speeds, this would provide nearly a full day's warning.) Such anomalies would not have gone unreported; they would be of universal interest to the scientific community. And because the planet's tides are highly predictable and heavily monitored, anomalies worthy of scientific examination would have occurred when the object was further still.
Factual error: Almost immediately after the brown dwarf fragment embeds itself in the Moon, the Moon moves 30 million km closer to the Earth. The brown dwarf fragment is said to have twice the mass of Earth. The result is that tidal forces due to the Earth-Moon interaction would be 200 times greater than our real tidal forces. This would cause widespread flooding as massive tidal surges affected coastal areas, an effect not seen in the film.
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