Goofs

Fowler points out that "nobody's bothered to paint over" the graffiti on the Endeavour. However somebody apparently did, and then also bothered to repaint it, as there are numerous differences compared to the writing seen five seconds earlier, before the cut, most notably the line thicknesses, the blobs on the ends of the letter K, the inclination of the F, M and N, and the distance between the C and the K.

(At about 18 min) The judge's nameplate starts out evenly aligned in its holder, but in a subsequent shot it's displaced to the left; then it's properly aligned again.

Cell phones and satellite phones would have all been dead after the disasters that took place. Cell towers are often the first thing to go in a real disaster, and it was shown that every satellite around the Earth was completely wiped out.. so sat phone certainly wouldn't have worked. The Moon doesn't catch all satellites because even when it is close, the surface area is very small compared to the Earth and it doesn't have 360-degree circulation at the right height in the approaching time.

The atmosphere acts as a fluid. If the atmosphere in one area is sucked away, the remaining atmosphere would flow into that area. At no point would there be a vacuum. However, if there were a vacuum, Tom's voice could not be heard as sound doesn't travel through a vacuum.

Fowler tells Hutchings, "The Moon has entered an elliptical orbit," when what she is trying to say is that the Moon has left its elliptical orbit and is now spiraling down to impact the Earth. Both of them, as NASA staff, would know that.

With the shuttle rotating so rapidly during the initial contact with the aliens, the astronauts would be subject to centrifugal force and wouldn't float around. They would be pressed against the walls and have difficulty moving.

White dwarfs are usually about the size of the Earth. The smallest possible size for one is still larger than the Moon. You couldn't fit one inside the Moon.

No, that's not the Empire State Building and One World Trade Center shown blocks apart. That's 40 Wall Street, which is indeed very close to One World Trade Center.

A light-year is a measurement of distance (the distance light travels in one year), not of time, so referring to the alien's technology as being "light-years ahead of ours" doesn't make any sense. The phrase "light-years ahead of us" is a common phrase to describe something which is more advanced than what we are used to. A light-year ahead of someone is far ahead, hence the phrase indicating that something is far ahead of what a society currently has. Claiming this as a goof is like claiming someone using the phrase "they dropped the ball" is a goof when there is no ball in the scene.

When Brian and KC are talking to each other while looking through the glass airlock doors, they are "floating" in zero gravity. However, the zipper on Brian's left glove is hanging down and swinging due to gravity.

Astronauts must wear gold plated protective visor and special sunshade during spacewalk to shield themselves from the harmful rays of the Sun. This would render their faces invisible for the audiences which is unacceptable for Hollywood.

In the chamber inside the Moon, Fowler and Houseman are looking away from a large door, behind them. When it opens, loudly, they take a full second to respond and turn round. In such an unfamiliar environment, you would expect them to be alarmed and react instantly.

The astronauts wear space suits but have normal boots.

Karen fires multiple rounds rapid-fire from a single shot bolt action rifle. No bolt action rifle is capable of firing at such a speed.

During the looting sequence, a brief shot of The London Pavilion at Piccadilly Circus is shown. This must be stock footage, as Ripley's Believe It Or Not can be seen. London Ripley's closed down in September 2017 and was replaced by Body Worlds, which unfortunately closed down for good on 17 March 2020 due to the UK COVID-19 lockdown.

The effect of the Moon is inconsistent throughout the film. People and cars are getting lifted by the gravitational pull while at the same time, debris of mountains hit by incoming Moon rocks fall down at full speed.

During the nuclear missile launch during the bunker scene, the general says to launch on three, but then he starts counting down from three to one.

Houseman says that the moon's surface gravity is "1.62 metres squared" That is a unit of area, not gravitational acceleration. He meant "1.62 metre per second squared." The whiteboard that he is pointing at has the correct unit.

On the phone to the observatory in Chile, Houseman says "I'm still tracking our [sic] Moon's orbit." Most people (including astronomers) would say "the Moon".

However, a character saying something in a slightly different way to what "most people" would say isn't a character error. It's still a valid comment and it's just the way the character speaks.

Houseman says "It's doing something to the megastructure's power source." Fowler asks "Excuse me, 'The megastructure'?" and Harper says "Please don't ask." Houseman proceeds to explain and Harper interrupts, "I told you not to ask." However, Fowler hadn't said another word. It was pointless telling her not to ask because she had already done it.