When Margo was trying to plead her case in season 1, she said she'd been at NASA since 1966. In season 2, ep 1, she has a 20-years of service certificate on the wall, in 1983, 3 years before her 20-year anniversary.
In the opening the sun rises on the moon way too fast. In real life, from the time the sun peaks over the horizon to the point it is fully visible would take over an hour.
A 'day' on the Moon is about 14 days long. Sunrise would be far slower than shown.
The solar storm was said to be moving at 30% of the speed of light, in which case it would reach the moon in less then a second after reaching Earth rather than several minutes later as depicted.
An Astronaut with spacesuit masses about 150kg, but on the moon would only weigh about 25. When Molly is dragging Wubbo to safety she is however shown straining under his weight..
When Ellen is talking to her husband the dialogue proceeds as if the 2.5 second delay in Earth - Moon communications does not exist...
The European Space Agency patch worn by the Canadian and European astronauts is incorrect. Austria did not become a member until 1986, Finland did not become a member until 1995, and all flags except for Sweden are the wrong way around.
During the recap of the time jump at the beginning of the episode, several news clippings use the Lorem ipsum placeholder text.
Many of the buildings on the Houston skyline did not exist in 1983.