In the shot with the two celestial objects in the sky, they are in different phases: 1 a little more than half, 1 a little less than a quarter. Given that they are illuminated by the same source, they ought to be in the same phase.
Becker is the last to go through the hatch into the NEB bunker, but when the camera switches to the view inside the bunker, Becker is seen already on the walkway while the others are still climbing down the ladder.
On the way out of NEB HQ, when Jefferson jokingly repeats the line "Can I come with you?" we see Hendricksson from behind as he points his rifle upward and away from Jefferson. When we cut to a front view, he is still pointing the rifle forward. Then we cut to a rear view again and the rifle is still pointed upward.
The pieces on the Game of Ur board shown in the first scene change from one camera angle to the next.
When Jefferson's lower barrel gets bent by the screamer, it only lasts a few frames and then is straight again.
When Hendricksson is the last one running out of Richard Cooper's command bunker, he falls in a large puddle of water, however, once he gets up, he is not wet.
The pieces on the Game of Ur board shown in the first scene are not laid out or played according to the actual rules.
When Hendricksson, Jefferson and David first meet the two N.E.B. soldiers, David is shot and you can clearly see the wire used to lift and pull David backwards into the snow.
(at around 47 mins) Just after the boy is shot, Becker says, "Who would shoot a snot-nosed boy with a hard luck story?" and there is a vehicle moving in the background, high up on a ridge, from right to left between Becker's and Ross's heads.
When we first meet Becker on the snow, a close up of his "Oakley Blades" shows, very clearly, the reflection of the camera crew.
Right after the baby nuke is launched, there is a crew member far off in the background. The "friendlies" are all in the same area and the "screamers" are all supposed to be dead, so it must be a crew member.