When Commander Koenig flies out to check the problems in Disposal Area One, the activity there lights up the sky in bright flashes from beyond the horizon. However, there is no atmosphere on the Moon, and therefore nothing to be "lit up". There would be no visible effect beyond line-of-sight.
A tremendous explosion on "the dark side" of the Moon supposedly throws the Moon out of orbit and into deep space. There really isn't a "dark side" to the Moon. Though it is true that only one side of the Moon ever faces the Earth, all parts of the Moon get sunlight as it orbits Earth every month. Even if they meant the "far side" of the Moon, the situation is no better. If they actually meant "dark" side (ie: the side facing away from the Sun at that moment) then the explosion would have flung the Moon into the Sun. If they meant to say "far" side, then the explosion would have flung the Moon into the Earth.
If the waste disposal sites were on the "far/dark side of the moon", the explosion would have pushed the moon towards the earth instead of directly away as the far side is the side that is always facing away from earth. (Note: Isaac Asimov admitted that that the moon could've spiraled out of its orbit around Earth, approaching to it closely, then shooting off away from the Earth. In addition, Year Two publicity placed Alpha's location within the crater Plato, which resides on the north end of the face of the moon, and judging from the toll of destruction the explosions had inflicted on the base, the waste area was apparently situated just over the moon's horizon. This would cause the moon's course to come close to the Earth, then spiraling away, as Asimov had mentioned, creating conditions similar to what the newscaster described at the end, as well as tidal disasters).
Within only a couple of minutes of the explosion which blasts the moon out of orbit the moon quickly begins to decelerate. Since the moon was moving through the vacuum of empty space there would be nothing - not even an atmosphere - to allow for any deceleration to take place.
Collins tries to smash his way out of the room using his helmet on a window looking out on open space. Such flimsy materials would never be used on outer walls or windows because of the obvious danger.
(About 4:43 in) When Nordstrom goes berserk on the lunar surface due to what they think is a virus, he picks up and throws the hapless Steiner. While he does this, his helmet visor opens for a few moments, which in real life would expose him to hard vacuum.
When Koenig instructs Carter to take the Commissioners shuttle, Carter calls in - announcing the ship as "Eagle 1". The number on the interior door says "Eagle 6". In addition, referring to this vehicle as Eagle 1 means there are now two ships with the same number. Alan should simply have said "Carter to Moonbase Alpha".
One of the shots in the "This Episode" sequence is of the rocks rolling down the hill from the second episode produced "Matter of Life and Death".
Further to when Carter is observing the Moon from space, Koenig had told him to take Commissioner Simmonds' Eagle. The number of the Eagle is, however, 6 - the same Eagle that Koenig crashed shortly before when observing Area 1.
Commander Koenig had incorrectly used the term "decelerate" when the crewmen were no longer pinned to the floor following the explosion. Koenig should've said "We're no longer accelerating" when they were able to move freely again. As Professor Bergman had pointed out, the explosion area had stopped fissioning, which had been causing the moon's acceleration. The moon was now traveling at a steady rate (neither accelerating nor "decelerating"), so the G-force effect was no longer present.
Time Error: when the commissioner Simonds calls Commander Koenig the clock shows 2:26 but when commander Koenig Calls Paul a few seconds later after Commissioner Simonds it's 3:53
In the episode, "Breakaway", a wire is clearly visible when a crewmember is thrown backwards. (Note: most likely, the "wire" being referred to is actually the antenna attached to the moon buggy, swaying around during the scuffle).
In this pilot, the globe in Koenig's office inexplicably has Sweden and Cameroon missing and replaced by expanses of the Baltic Sea and Atlantic Ocean respectively. It seems that the error was eventually spotted, as later in the series the globe was always placed with the Americas facing the camera. (Note: The geographical errors on the globe are the result of it being hastily painted over for filming; Martin Landau considered its original colorful appearance to have looked too gaudy on the set and demanded that it be repainted in colors that would blend in with the surroundings).
Commander Koenig tells the Alpha crew that attempting to return to Earth would fail due to a lack of travel plots and resources. This makes no sense because they know where Earth is in relation to themselves, as their movement out of orbit had been linear, making their "travel plots" simple, and the only resources they would need for an emergency escape would be the Eagles, which they still have plenty of. (Note: although it wasn't clearly explained, the reason Carter had used the Commissioner's Eagle to observe the waste area's operation was due to their own Eagle fleet being in the process of being converted into platform utility vehicles to transport the waste canisters - "they're all committed", as Alan explained when Koenig ordered him to commandeer one of their Eagles).
When Commander Koenig first discusses the virus with Dr. Russell, Barbara Bain refers to Koenig as Commander Russell.