When the crew starts licking the Presidents' heads, Dr. Cahill's top under her lab coat changes from purple to white and back again between cuts.
When they show Paul Revere's midnight ride, he says "the British are coming, the British are coming." The real-life Paul Revere did not say this as it would make no sense since all the colonies at the time were British land. What he really said was "the regulars are coming, the regulars are coming."
The Professor states his ancestor Philo Farnsworth as inventor of the television. Though the real Philo T. Farnsworth did make several contributions to improving television it was actually invented by British engineer John Logie Baird.
Bender complains about being used as a lightning rod, but in Season 1's Hell Is Other Robots (1999), he enjoys electricity so much he becomes addicted to it.