Character mistake: Captain McCrea tells the passengers that it's the 700th anniversary of the Axiom's first flight. The Axiom has been in flight for 255,642 days. Actually, 700 years is 255,675 days. That figure includes the additional day in 175 leap years.
Suggested correction: Leap years only occur because of the earth's rotation around the sun. As the AXIOM is in space, there is no need to correct for the earth's rotation.
First, rotation is the spin of the Earth (which cause day and night). Revolution is the earth orbiting the sun (which causes years). However, this correction is not valid on the premise you're trying to present. Many films set in space still use Earth time, so a day is 24-hours, even though they're in space and there is no sunrise and sunset (although it's stated the Axiom operates on a 25-hour day). So they would use Earth's year, which takes 365.256 days. Since the Axiom isn't orbiting the Sun, it wouldn't experience a year, so they're using something else. The fact that they're slightly off suggests it's a writing mistake and there's no evidence they use an arbitrary 365.203 day year.
That's still wrong. Even if their years were strictly 365 days, 700 years would be 255,500 days, not 255,642.
