Factual error: During the 31st year of the Avalon's voyage, the ship passes close to the star Arcturus, which is about 37 light years from Earth. Later in the movie, it was stated that the Avalon was moving at around 50% of the speed of light. The ship would not have reached Arcturus in the time allotted.
Factual error: The Avalon generates its gravity by rotating, which is made evident by the fact that the elevators connecting the three helical pods are without gravity. When the passengers go spacewalking, the instant they walk out the airlock, they have to be secured by magnetic boots. When they turn them off, they become weightless. Both assertions are wrong for the same reason: If the gravity is created by centrifugal force, that force is present on all points of the ship with the strength depending on the distance to the hub of the ship, no matter whether that point is inside or outside the ship's hull. That of course includes the ledge in front of the airlock. Any surface that is oriented towards the hub of the ship is felt as "floor", surfaces radially oriented to the hub would feel like "walls", surfaces oriented away from the hub would be "ceilings." So if you step off a ledge on the outside of the ship the way the actors do, you'd be drifting away from the ship on a tangent to the ledge you stepped off, and end up hanging by your tethers. You wouldn't accelerate away from the ship like you would in a real gravity field, but you would float away with a speed equal to the acceleration simulated by the artificial gravity. The only way to become weightless would be to cancel the sideways motion imparted by the rotation of the ship. At the rotation speeds depicted in the movie, that would take at least a motorbike to do.
Plot hole: In multiple scenes in the movie the starship is in a gentle rotation which allows 1G gravity on the ship. When the power to the propellant is cut the rotation stops and gravity is lost. Such a design for a starship doesn't make sense as the entire structure could be put in a continuous motion, as is indeed done with many probes today without requiring the continuous addition of power. Even if this design was chosen with part of the structure fixed and party of it moving around it still seems unlikely that the rotating part would come to a grinding halt within seconds (if it did, the friction of the structure would be huge, requiring enormous levels of energy to keep it moving) The only reason the movie chooses this unlikely design is to integrate the crucial shot of Aurora floating out of the pool when power is first lost.
Continuity mistake: Immediately after Jim sends the emergency message back to Earth, we see a long, overhead shot of Jim slowly walking through the Grand Concourse. To Jim's right the doors to Arthur's bar are visible (towards the top of the screen as viewed from the audience). All the doors are closed. The camera then cuts to a close up of Jim as he continues along the Grand Concourse and to Jim's right we can see into the bar and all the doors are now wide open (not in the process of opening, but instantaneously and fully open).