Factual error: In the PALOMINO scenes, Anthony Perkins wears a long lab coat. In most of the scenes, it hangs straight down; but in the low gravity aboard the ship it should be flattering about (that's why such loose garments are not worn by real-life cosmonauts; they would be a hindrance).
Factual error: In the opening sequence the crew of the Palomino choose to approach the U.S.S. Cygnus, and thus fire the ship's rocket motors to accelerate it towards the target. As the motors push the ship, Kate McCrae is seen maneuvering herself in a state of zero-g. Very soon after that, she is seen floating weightlessly as the ship once again fires the engines to accelerate away from the nearby black hole. In reality, there'd be no weightlessness onboard the ship during any rocket generated acceleration. Everyone would be pressed to the floor.
Factual error: In one scene, Mr. Booth is touring the Cygnus by himself and finds a control room for the ship's botanical garden. He goes to a window to look into the garden, but the pane is fogged over so he wipes it clear with his shirt sleeve. Dew will form on the hotter, more humid side of the window, his side ought to be dry.