Plot hole: It becomes quite obvious as the movie progresses that the aliens want to capture and use (or digest) humans, so it defies logic that the first one to appear immediately starts vaporizing every human in sight. Since the people posed no threat, the only reason to vaporize them would be if the aliens simply wanted to be rid of them - which they obviously didn't. So this initial vaporization was simply a manufactured plot device by the movie makers.
Suggested correction: There are plenty of humans to go around. They don't need all of them. What they first wanted to do is collapse human society. That usually works if you start killing indiscriminately.
Maybe they needed 20 billion people. So we don't know that there "are plenty to go around." And again, the people they vaporized were no threat. And they didn't need to "collapse human society" (and you have no way of knowing what they "wanted" to do); they merely needed to remove threats. So, again, it defies logic to unnecessarily vaporize what's later shown to be desirable to them, if not required by them.
You don't know what the wanted to do either. Seeing them kill so many people, logically shows that they don't need all those people.
Suggested correction: Doesn't defy logic in the slightest. It seemed pretty obvious to me that the initial "invasion" (vaporizing every human in sight and starting battles) was to disrupt and take control of the human population. Thus making it easier to harvest human blood/tissue from the remaining population. (Which, from my memory at least, were implied to basically be used to fertilize their terraforming efforts/the red weed.) If you wanna take somewhere over, you can't just wander in and say "Ok, this is MINE now!" That's not how war works. You have to show force, assert dominance and then get rid of any possible opposition.

Continuity mistake: When the asphalt in front of the church starts to crack and move and Ray gets on the sidewalk, his legs are positioned in different ways in two different shots. (00:22:36)
Suggested correction: With the way Ray moves his feet (hopping/dancing quickly from one foot to the other), I don't see a discrepancy.
If you look closely in the first shot he keeps one foot on the asphalt and the other one on the sidewalk, in the other shot he has both of them on the sidewalk, so the discrepancy is very evident.
Other mistake: When they arrive at the ferry port the crowd try to steal the car and it all turns violent, as if no one's seen a car for a while, but when they arrive on foot at the ferry there are several cars already on it, and no one bats an eyelid. The cars at some point must have driven through the crowd with no problems. Also the cars are taking up much needed space on the ferry.
Suggested correction: The cars could have been on the ferry before the crowd arrived. Or at least have been standing at the front when the ferry arrived. Besides, the fight over the car is for people not going onto the ferry obviously, but going somewhere else.