Character mistake: Sybok tells Kirk that no one believed the world was round until Columbus proved it. Someone who studied at the Vulcan Academy should know that the Greek philosophers had proved the world was round and calculated its circumference centuries earlier. Columbus never set out to prove the world was round, just to find a shortcut to India.
Character mistake: Near the end of the film, Kirk mentions that he had a brother once, to which Spock appears surprised. Kirk then responds that he was lucky to get him back, referring to Spock's death and rebirth in the second and third films. One problem - Kirk DID have a brother, who died at the end of the original series' first season. Spock doesn't seem like the kind of person to forget about such things, especially as he was nearly killed by the same parasites. Spock's memory may still have been incomplete, although you'd think he'd know such a major detail about his best friend. However, McCoy should definitely remember Kirk's brother, especially seeing as he was the one who pronounced him dead.
