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.
Character mistake: After sleeping with Juan Antonio, Vicky returns to the library to study and do research. The narrator says that she cannot stop thinking about Javier, the actor's real first name, not the name of the character Juan Antonio.
Character mistake: When Carl answers the door to the LDS missionaries, they are not wearing their black name tags.
Character mistake: When Will finds April's lost copy of Jane Eyre, the book shop clerk reads the inscription written by April's dad and says it's a quote from the book. It's actually a quote from Bronte's poem Evening Solace.
Character mistake: During the Nativity play, Pastor Phil says, "Are we ready to see the result of the Immaculate Conception?" The term 'Immaculate Conception' refers to the conception of the Virgin Mary (conceived without Original Sin), not to the conception of Jesus. Furthermore, the Immaculate Conception is a dogma of the Catholic Church, and not something which a Protestant pastor like Phil would believe in.
Suggested correction: The immaculate conception refers to Mary conceiving Jesus. It was Immaculate because she was a virgin carrying God's child. The Virgin birth (Jesus birth) is in the New Testament and every Christian (Protestant and Catholic) believe the story of the Virgin Mary and birth of Jesus.
The Immaculate Conception is indeed the belief that Mary was born without Original Sin (and thus was immaculate, meaning spotless or clean), although some religions teach Mary was born in sin and made immaculate through the Holy Spirit. The birth of Jesus is known as the Virgin Birth (one could even use the phrase "virgin conception.") Immaculate Conception has nothing to do with being born of a virgin.
Character mistake: During the seminar, Professor Rohl tells students that only 19 workers of Auschwitz were sentenced (in 1966). During the first trial of Nazis from Auschwitz, 39 were sentenced, including 23 persons condemned to death. The trial was in 1947 in Krakow.
Character mistake: McQuarry enters the subway at the 103rd Street station on the 1. He is transferring to the 2/3 at Chambers Street when Bose approaches him. However, it makes no sense to transfer here. As someone who knows New York, McQuarry would transfer to the 2/3 at 96th Street to benefit from the express ride to Chambers. (01:03:05)
Character mistake: When the young boy is attempting to hack, Marriage Registry is spelled Wedding Registery. (00:10:56)
Character mistake: Tom goes with Hannah to meet with the reverend who will be conducting the ceremony. Hannah (and the credits) say his name is Rev. Feiten. However, Tom refers to him as Rev. Flint.
Character mistake: At the rehearsal dinner, when Steve walks up to Miranda she calls Steve "Dave." Dave is his real name.