Factual error: In one scene they attempt to divert the ship by manually activating the ship's bowthruster. A thruster is a propeller in a transverse direction. This allows the ship to turn more efficiently when docking. However the thruster loses any efficiency above approximately 5 knots. In the film they use it at 17 knots. Secondly, a thruster is powered by an electric motor of at least 500 kW, yet they manage to turn it by hand. That handle does not exist in real life, and no one would be able to turn it anyway.
Continuity mistake: You have to look really close, but while they are dancing, when the alarms go off, Sandra Bullock is wearing hose. Later, when they are running around the ship, she has taken them off. Then towards the end, wear she is under water, with her hands tied together, she is wearing pantyhose again.
Factual error: You cannot walk into a ballast tank from the accommodation areas. The tanks are not painted white on the inside, and electric lights are not installed in ballasttanks. And finally, when filling ballasttanks, it is done through a pipe and a pump, not by opening gigantic doors in the ship's hull.
Factual error: Near the end, the starboard anchor runs out, into a car on the pier. The anchor chain on a normal vessel of that size is about 300 meters long, and fastened to the vessel at the end, in the bottom of the so-called chain-locker. And the anchor does not come out of the ship in a roll lead, it has its own opening in the hull.
Factual error: The Eindhoven Lion exploding should almost be akin to a nuclear bomb going off. The boat they escape on would have been incinerated from the blast, or at the very least blown off the water.
Plot hole: When Drew first went into the elevator, Geiger's clock on the countdown for evacuation said 5 minutes about. When Drew gets stuck in the elevator when Geiger blows up the charges he positioned throughout the ship, the countdown on the computer had stopped already. How could Drew be in the elevator for five minutes, if not longer? It wouldn't take 5 minutes to get up a couple of floors.