Character mistake: Chick Gandil mispronounces Eddie Cicotte's name, calling him "Si-coty" instead of "See-cot."
Character mistake: While pitching his shrinking machine to NASA Szalinski claims that reducing the size of a rocket's payload would result in "staggering" savings in the fuel required at takeoff. However, he makes it clear that his machine works by reducing the space between atoms, meaning that the shrunken object weighs the same as the original. Weight is the critical factor in calculating fuel consumption, not size. Anyone at NASA would pick up on that instantly.
Character mistake: At the psychiatric ward, Ray says that Vigo is a XVII century tyrant; it's not a very fitting way to describe him, since he saw the XVII century for just a decade; as the book mentioned, he lived from 1505 to 1610 and was the scourge of Carpathia for the XVI century. (01:16:15)
Suggested correction: Not a mistake, Vigo was a tyrant in the 16th and 17th centuries, Ray chose to label him a 17th century tyrant because that's the century he died in. It would be like calling Osama bin Laden a 21st century terrorist, which is correct, even though he also committed terrorist acts in the 20th century.