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.
Continuity mistake: Throughout the movie, the cameras show a wide shot of the cruise liner from the sky, the evening before all the commotion look for the name of the ship, it is painted over, but the next morning, the name is perfectly readable.
Continuity mistake: Before the Eindhoven Lion explodes, there are several shots of lifeboats being lowered to the sea, but in all subsequent shots around Eindhoven Lion, the lifeboats are nowhere to be seen.
Continuity mistake: When Annie is being taken hostage at the end, Alex jumps down onto the stern door but misses and lands in the water. He is then shown hanging onto the stern door's edge. Since the edge is about 10 feet over the water's surface, he must be a pretty good athlete to jump and grab hold of it. (01:23:10)
Continuity mistake: On the bridge the speed is shown going down fairly fast. The camera shows it going down from 17.8kts to 17.3kts. Geiger is then made aware of the deceleration and opens up his PC. The speed is still decreasing but is only at 17.1kts when he first looks. The speed is still going down at the same rate so should be well past 17.1kts on Geiger's screen. (01:18:00)
Continuity mistake: When the cruise liner is heading towards the oil tanker, her speed is 17kts. When the oil taker is monitoring the cruise ship, the speed it's doing is 14kts. Alex's attempt to slow the cruise ship down failed so that won't explain the difference. (01:18:00 - 01:21:00)