Factual error: In the scene after Zefram's ship goes to warp, when the ship is being turned around to return home, Cochrane remarks "Is that the Earth? It's so...small." He wouldn't have been able to see it, provided the distance the ship just flew. Warp 1 is the speed of light and in a 1 minute flight, the Phoenix would have travelled over 10 million miles - at that distance the earth would just appear like a bright star.
Factual error: In the scene where Troi is drunk and Riker asks if Cochrane can accept the truth, it is night. Then the scene switches to the Enterprise orbiting Earth over north America and it is apparently daytime because the sun is shining over north America, where the movie takes place. (00:31:05)
Factual error: When Zephram Cochrane, Riker and LaForge activate the warp drive of the prototype starship Phoenix, the prismatic starscape is seen streaking past (same effect as in the Star Trek: TNG series). However, the Phoenix never leaves the solar system or even the vicinity of Earth, achieving only Warp One (the max velocity of the Phoenix) for a few seconds. Even at lightspeed, the Phoenix did not enter interstellar space nor pass any other stars; therefore, the starscape should have remained almost motionless.