When Cmdr. Koenig is walking through the medical unit where his other self is dying, a close-up shot of his monitor has his name misspelled "KEONIG" but on a longer shot it is spelled correctly. (Note: One could argue that this was done as a hint to Koenig that this was not the real Alpha).
The Eagle Koenig, Carter, Victor and Sandra are in is identified as Eagle 1, yet the sign on the cockpit door says Eagle 4 and after the crash this becomes Eagle 6.
At one point the nameplate on Commander Koenig's medical monitor is misspelled as "Keonig". It is spelled correctly in other shots.
Raan informs Commander Koenig that Zenno is located five million light years away from Earth. This would put Zenno well outside the limits of the Milky Way galaxy, in empty intergalactic space. However, beyond Zenno's solar system, other stars can be seen. Worse, Raan shows Koenig a view of his city and the moon is featured prominently in the background, which would mean that the moon is also well outside of the Earth's galaxy, which is highly doubtful.
Even though Alpha is primarily a civilian installation, there still would be an established chain of succession should the base commander be killed or incapacitated. Thus, Alan's argument with Paul and Victor over who should lead the Alphans shouldn't take place.