Factual error: The astronauts land on an asteroid said to orbit a binary star 655 million miles from Earth. This is impossible, as that distance would place them well within our solar system. In fact, they'd be inside the orbit of Saturn, where of course there aren't (nor could there be) any extraneous suns. The nearest star to our system is, in fact, trillions (not millions) of miles away. (00:02:15 - 00:04:00)
Factual error: When McCauley and Rennish find the body of a previous moon explorer, they play back a message he left on a portable tape recorder. But they shouldn't be able to hear this: there's no atmosphere on the moon to carry the sound waves. Even if there were, their pressurized, self-contained spacesuits would still prevent them from hearing the tape. (00:19:30)