Other mistake: With how fast Alexander is traveling through time, when the pendant falls out of the time machine, he shouldn't be able to see it fall or hear it hitting the ground.
Other mistake: When Vox, the New York Library database, is bidding farewell to Professor Hartdegen, it states, "live long and prosper" while holding up the hand shape Mr. Spock used in the original "Star Trek" series. It is produced incorrectly. The thumb should not be next to the forefinger. It should be extended at an angle from the other fingers, so the hand represents the Hebrew letter "shin." This, as Leonard Nimoy has explained, is derived from a hand gesture used by Orthodox Jewish rabbis during blessing rituals.