Towards the end, when Orson Bailey is shot, he falls to the floor. When just the upper body is shown, there's a rug under his head. In wider shots, it appears as though the rug is near his feet.
Skouris blasts through a door where we find the extras have not started moving yet.
Before her abduction Maia drops her flowers twice.
When Bailey experiences his 'seizure' in the nursing home, the position of the cart and peg board are way different from the end of his seizure, to the very next shot.
The sound of the exploding missiles can be heard as they strike the comet. Since light travels faster then sound, it would be quite some time before the sound would reach earth.
The whole missiles-fired-at-comet part is wrong: the missiles are shown to impact their target mere seconds (or at most minutes, if we give continuity some slack) after launch. Later, we see the comet fly past the Moon towards Earth. It would take even the fastest rockets at least hours, and more realistically 1-2 days to get there, and standard ballistic missiles can't do it at all. Additionally, the comet is stated to travel at 3,000 km/s, which would bring it to earth in less than two minutes instead of the stated half hour. It would also be very, very hard to hit by missile at all at that speed.
The little girl Maia is collecting flowers in the woods. The flowers are clearly already cut with scissors or a knife and stuck loosely in the moss.