Factual error: On board spaceship Discovery, the crew's living area is the spinning centrifuge, which spins about its axis to generate a gravity-like acceleration at its perimeter, the floor. When exiting the centrifuge a crewman climbs a ladder from the floor up to the hub, where there's a door leading to other parts. When Poole & Bowman climb this ladder, it's evident that they're under full body weight the whole way up. But in reality they'd get steadily lighter toward the hub. In fact, they'd be practically weightless within a few feet of it.
Factual error: There's one scene where Charly's just woken up from his surgery. The next scene shows him working on a puzzle, and he has a full head of hair and no bandages. If he'd just got brain surgery, don't you think he'd still be wearing bandages or at least have his head shaved?
Factual error: The truck's gas tank is said to be empty, but is able to explode spectacularly later on. An empty gas tank may spout a jet of flame, but will not have enough force to rupture and damage the truck, a full tank of liquid gas will not burn unless vaporized. Simply put the truck would not explode in that Michael Bay fashion.