Factual error: When the Victorian astronauts are on the moon they are dressed in deep sea diving suits - without gloves.
Visible crew/equipment: In the scene when Bedford hits the ceiling in the Cavorite-covered chair, the thick metal cable attaching the chair to the ceiling is visible to the right of Bedford. It is NOT, as I initially suspected, part of a lamp or some other bit of scenery - at one point you can actually see it move as it pulls Bedford up and down.
Other mistake: The sphere operates through the opening and closing of Cavorite blinds to negate the force of gravity. It has no engines at all. Why then, when it lifts off from the moon, do you see a blast of what appears to be rocket exhaust?
Continuity mistake: Watch carefully as Bedford falls through the crystal prism into the underground city. On the surface he has his helmet on but in the very next shot, as he plummets down, he has no helmet. He explains that it must have 'fallen off' but you do not ever see it doing so. As the helmet would have to be twisted to be released, and no such action took place, it cannot have come loose.
Other mistake: Because there is no air on the moon, Cavor advises Bedford to touch helmets when they speak, otherwise they will not be able to hear each other. Yet there are several times where they seem able to communicate without doing so.
Suggested correction: Is this really a mistake? H G Wells wrote "The First Men In The Moon" over 1900-1901 before the invention of the aeroplane, when space travel was still a fantasy. By 1964 Yuri Gagarin and Valentina Tereshkova had flown into outer space, so the makers of this film knew what sort of equipment would be needed if you really wanted to make a trip to the moon. And this film shows astronauts in suits copied from those worn by actual astronauts. But the idea of the original book, and this 1964 film, was that a (very) eccentric English Victorian scientist led an expedition to the Moon. So, surely, if Victorian Englishmen and Englishwomen went to the Moon, they would have used the technology available at the time. Beside that, when they reach the Moon they find it is inhabited. Even in 1900 astronomers knew there was no life on the Moon. I don't think this film was meant to be taken too seriously, and that when they made the film they deliberately dressed the cast in deep sea diving suits as a joke.
Rob Halliday