Continuity mistake: Whilst looking for the ship on the glacier, the team varies between 9 members to 6, then back to 8. (01:49:00 - 01:49:33)
Factual error: The Academy of Sciences Glacier is at 80° north latitude, which means the sun doesn't rise at all between Oct 21 and Feb 21. Dan visits in Dec/Jan (his suburb is still covered in Christmas decorations when he gets home) but the sun is well above the horizon in Russia. (02:07:18 - 02:07:53)
Plot hole: So humanity in the future managed to solve time-travel, but is unable to develop armor-piercing, exploding ammunition? And it uses old, untrained civilians as soldiers to fire M16-16 and WW2 heavy machine gun ammunition at fast moving targets, instead of developing rapid-fire computer-targeted guns? The movie shows 0.5" ammunition (from said WW2-era machine gun) CAN take out the Aliens, so? (Not to mention flame-throwers, shown as effective but sparsely used, no tanks, etc).
Suggested correction: The rifles the civilians are equipped with aren't M-16s; they are modified BCM carbines "MK III" and "MK IV" with HERA Arms CQR furniture.
Plot hole: Dan returns from the future with a vial of toxins with him that can kill all the white spikes. He tells somebody to start mass-producing it but this information is not spread across governments or even made public, but it is the one thing they have that can prevent humanity's extinction and making people aware of that will stop the rioting.
Suggested correction: It isn't shown that this information isn't spread across governments, but it might have happened. It's possible that it was shared, but the storyline doesn't follow that journey because it had no impact on the plot. It's just an assumption that it wasn't.
