Factual error: It is not possible that Pitt could have gone up to the ship when it was already blasting off. There was literally fire in the tunnel.
Factual error: When driving across the moon, Brad Pitt waves his hand through lunar dust that's floating in the air. But there's no atmosphere on the moon to suspend dust like that, even if was kicked up by another buggy - it would fall straight back down.
Factual error: From the continuity of the movie it appears that the response from LIMA came within a few minutes of the transmission from Mars. This would be impossible. Even if Mars and Neptune were on the same side of the Solar System, in a straight line, they would be 4 light-hours apart, meaning the replay could not be received less than 8 hours after transmission. There's no implication that they kept Brad Pitt sitting in a room for 8 hours waiting for a reply.
Factual error: Pitt and the other astronauts fight at zero gravity during the take off. However, they are under acceleration, so they wouldn't be able to move.
Factual error: Cepheus is moving at immense speeds to make the journey at the speed it does. But despite the great speed, it seems to have no problem slowing down on a whim for a mayday, then speeding up again to get to Mars. And if it's got that much power on hand, what are all the solar panels for?
Factual error: The Cepheus appears to be under continuous acceleration on the way to Mars, and to Neptune. That would be the only way it could travel so far so fast. So, there would not be weightlessness any any time on board the ship, unless the engines were turned off.
Factual error: There no explanation given for why Cepheus does not have enough fuel to return to Earth. It would have been refueled on Mars and sent on a mission to Neptune. They wouldn't have sent it without enough fuel to return.
Factual error: In the movie, Neptune is shown having bright, wide rings. While the planet does have rings, in reality, they are very faint and thin. They were barely visible even from Voyager 2's flyby of the planet in 1989. They are nowhere near as big and bright as seen in the movie.