When Bedford releases Kate from her glass prison by smashing the glass with his rifle, the crystal pillar to the left wobbles slightly. As Kate exists the chamber, her dress hem catches briefly on a lower crystal structure revealing it to be just a two dimensional facade that flaps briefly as she passes.
When Cavor is momentarily stuck in the rocks on the moon's surface, he calls out SOS. A proposal for a distress signal was not proposed until 1903, and the SOS signal wasn't adopted until 1905 by the Germans and worldwide in 1908.
When taking a large leap on the moon, Cavor says "Geronimo!" four decades before it actually came into usage by US paratroopers during the second World War. The custom invoking the name of 'Geronimo' while jumping dates from August 1940 and is attributed to Pvt. Aubrey Eberhart, a member of the US Army's parachute test platoon at Ft. Benning, Georgia. There is a second explanation of the origin of the practice but it also involves US paratroopers of the 501st at Ft, Benning, Georgia the same year.
(at around 20 mins) Bedford puts Cavor's bicycle in the car. The handlebars of the bicycle are close to the car steering wheel. Seconds later, when he arrives at Cavor's house, the bicycle isn't in the same position; its handlebars are now "outside" the car (it's the front wheel which is now close to the car steering wheel).
(at around 1 hour 27 minutes) Cavor is climbing the stairs to the Grand Lunar. We can see his left calf, while the right one is covered by the trousers (or socks). Next scene, when he arrives at the top of the stairs, we can see both of his calves.
Kate and Cavor enter the room of the large white sphere and the door closes behind them. Later, Bedford forces the same door, and leaves it partly opened.
Next time we see it again, it is now closed. Later again, when Bedford and Cavor are escaping, the door is partly opened as before.
When Bedford goes up to the ceiling in the chair painted with "Cavorite", it supposedly gets caught in a wire and pulley system holding up a rod, but a closeup view makes it obvious the wire and pulley system is actually there to hold up the chair, and the rod is just a way to cover for it.
Even supposing that 19th century deep sea diving suits could have let the 19th century astronauts move about and breathe on the moon, their hands were left uncovered. Over the course of a few minutes, the hands would swell and become too painful to use, as happened to Joseph Kittinger due to an equipment failure during a very-high-altitude balloon ascent in 1960. In addition, unfiltered ultraviolet solar radiation would burn their skin in the sun, and touching any shaded objects (which would be very cold) would freeze their exposed hands.
We see the Selenites kill the large carnivorous centipede like creature with a death ray of some sort. All life on the moon is referred to as 'insects' and depicted as over sized insects with exoskeletons. In a subsequent scene the giant centipede is stripped of soft body parts and internal organs revealing an oversized internal skeleton of bone for dramatic visual effect (a redundant skeletal system an insect would not have).
The moon race, the 'Selenites' are referred to as insects. They do have wings, antennae and compound eyes characteristic of insects but are shy a pair of legs, do not crawl or fly and walk upright on their hind legs.
When Bedford and Cavor follow the tracks of their missing sphere to the zigzag door where, after much difficulty, they enter. They see the tunnels and then we see them continuing on walking through another zigzag door that wasn't there just before. Many zigzag doors of the same design are used throughout the cavern. However, Bedford has no problem prying them apart as he had with the first door.
Arnold Bedford invests money in boots from the Boer War, speaking as if this war is in the past. Most viewers think he is talking about the Boer War of 1899-1902, which began after this scene takes place. However, there was an earlier, less-publicized Boer War in 1880 and 1881, which could be what he is referring to.
When they're on the moon during daylight it is thought by many that they shouldn't be able to see stars for several reasons. The moon is about the same distance from the sun so it is receiving the same light intensity as Earth. One of the reasons we don't see the stars on Earth during daytime is because the sun's brightness over powers the magnitudes fainter light from distant stars. Although the moon doesn't have an atmosphere like earth to diffuse the sunlight during daylight hours it does have a much higher albedo than the earth does. Its bare light colored rock surface reflects much more of the sun's light back into space than the earth's surface covered by forests and oceans absorb, although cloud cover does give a higher albedo than the moon has. However, albedo and a lack of atmosphere will not impede starlight.
When Bedford and Cavor first fall through the transparent covering into the deep cavern and Bedford swings himself towards safety, his legs can briefly be seen to pass behind the foreground matte painting (behind the shadow of the platform).
When the modern day astronauts find the British flag on the moon having been left on there for as long as it was supposed to have been all of the colors should have been bleached out making it white or at least very pale with no atmosphere to protect it from the sun's ultra violet and infra red waves.