Factual error: While the Leonov has a centrifugal section to simulate gravity, the ship's bridge is not part of it (evidenced by the stationary views outside its portholes). Yet in various scenes, including the one when Floyd rushes in to discuss his plan to return to Earth sooner with Tanya, gravity seems quite evident. Floyd marches across the compartment onto the raised pilot area's floor, then steps down from it, his foot landing audibly. Tanya's open jacket also hangs down normally as she moves about. Yet when Floyd demonstrates his plan using two pens, they float in mid air.
Factual error: In the vast majority of cases, U.S. Astronauts wear the US flag on their left arm. On the rare occasion the flag is on their right arm, the flag is reversed so that the blue field remains toward the front of the person wearing it. The patch on Dr. Chandra's space suit during the launch countdown to leave Jupiter is on his right sleeve but is a left-sleeve patch.
Factual error: The filmmakers here forgot how a centrifuge works to mimic the effects of gravity. It is centripetal force wherein an object is pulled away from the center of rotation (you feel its effect on a merry-go-round when it spins really fast and you are tossed off by the centripetal forces). No gravity is actually created. So when the two astronauts are walking along the outside of Discovery and Curnow announces he is getting heavier, it is impossible. First, he's not within Discovery (and if he were, the force would pull him toward the ends of the ship - correctly depicted later when the men are shown walking on the inside of the pod bay doors). The area they are walking on is dropping away from their feet. Both men should be motionless in space as the ship falls away 'below' their feet, then rotates around and kills them when it clobbers their heads half a rotation later.