Factual error: Near the end of the episode, the full moon is shown in the daytime sky, well above the horizon. This is impossible, as any celestial body lit by the Sun has its full phase only when it is directly opposite the Sun; thus, a full Moon rises at sunset and sits high in the sky only during the night. For the Moon to be in the sky during the day as shown, it would have to be visibly of a phase other than full.
Suggested correction: The moon is not actually completely full. It's in a gibbous phase (opposite of a crescent), which can indeed be seen in the daytime.
Factual error: When Clara is watching the Earth through binoculars in order to see whether people left their lights on or off, the planet is rotating at an impossibly high speed. (00:36:15)
Factual error: In this episode, it is stated that the Moon's sudden increase in mass caused a devastating global high tide. The amount of the increase in mass is given as 1.3 billion tonnes. But the Moon has a mass of over 70,000,000,000 billion tonnes, or over 50 billion times the supposed increase. Such a negligible increase in mass, less than 0.000000002%, would have almost no effect on Earth's tides, let alone be devastating. (00:20:46)
