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: 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.
Character mistake: During the debrief meeting with the generals, Roy states the Lima Project was "some 29 years ago" and "the ship disappeared approximately 16 years into the mission." A few minutes later, Roy narrates "I was 16 when he left, 29 when he disappeared." This of course is only 13 years into the mission. (00:11:27 - 00:15:03)
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.
Character mistake: Brad Pitt has control jets on his space suit - he uses them to accelerate him back towards his ship at the end, but somehow doesn't think to turn himself around and use them to slow down, hence slamming into the ship at great speed. Given the skill he demonstrates every other time in the movie, this only seems to happen for the sake of a dramatic arrival.
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.
Character mistake: When Cepheus stops accelerating (which it would not have done until it turned to decelerate) crew plays in zero G's like amateurs who had never been in space. They were described as professionals with a lot of experience. They would never have risked fluid in the electronics by doing what they did.