Factual error: When the Immortality Gate is activated, there's a wide shot of Earth as the wave from the device goes around the planet. In another instance of a mistake made by a few previous Christmas specials, despite this taking place on Christmas Day, the North Pole is looking very, very sunny for what's supposed to be the dead of winter. (00:54:50)
Factual error: The Vinvocci ship is said to be orbiting 100,000 miles above Earth, later refined to 105,000 miles. That's one-third of the distance to the Moon, and the Earth's apparent size from the windows of the ship is far too large for them to be that distance, or even 100,000 kilometres above the Earth's surface. Judging by the Earth's apparent size, the spaceship is actually orbiting 6,000-7,000 kilometres above the planet's surface.