Dr. Logan states that the first man in space Yuri Gagarin was unmarried and that the first married man in space was Alan Shepard. This is incorrect, as Gagarin was wed to Valentina Goryacheva from 1957 until his death. Shepard married first, however, marrying Louise Brewer in 1945.
Viral pneumonia requires an incubation period. Somehow, after the trio had regained consciousness following their transportation, Helena was already infected.
Dr. Logan states that a galactic eclipse will take place, meaning an entire galaxy will be moving between the Milky Way and whatever galaxy the moon is currently home to (The Taybor (1976) confirms that the moon is no longer situated within the Milky Way galaxy), blocking communication between Texas City and Moonbase Alpha for decades. The problem is that galaxies move so slowly, it would take hundreds of years (if not thousands) to achieve such an effect. To complicate matters, Maya confirms Dr. Logan's findings, only she states that an entire "constellation" will be blocking communication. There's an enormous difference between a galaxy and a constellation; the least of which is that a constellation is a perceived grouping of stars as seen from a particular point in space, usually placed within a planet's celestial sphere, and not a true star cluster.
When Koenig, Helena, and Alan are viewing the moon through the clouds, the script has Alan erroneously referring to Copernicus - an enormous crater - as a mountain.
Due to being attacked by a man using a real sword, Nick Tate had a stunt double. However, the stuntman more closely resembles Prentis Hancock.
The Alphan trio had been transported to 1339 Scotland. It's stated that the pandemic Black Plague had been ravaging the countryside well before the Alphans' arrival. However, historically, the plague hadn't reached the British Isles until 1348, and Scotland even later.
MacDonald (the Scottish clan chief) assumes Koenig and company were from England due to their language and had learned it himself from conversing with English prisoners. However, the spoken language of England in 1339 sounded more like French.
Earth broadcasts to Moonbase Alpha using a technology called "neutrino transmission." Alpha should have been unable to respond, though, since it does not possess this communications system.