Factual error: The EMP burst would have only affected a small number of vehicles. Most vehicles act like a Faraday Cage.
Other mistake: The military personnel are part of the "Army", but wear USMC uniforms.
Factual error: At the onset of the Third Wave (avian-transmitted disease), Chloe Moretz narrates: "There are over 300 billion birds in the world. That's 75 birds for every person." Apparently, the screenwriters couldn't use a simple calculator. Given that the movie is set in the present (with our current human population of about 7.4 Billion), the ratio of birds-to-people can only be about 43 birds for every person, if we accept the film's "300 Billion birds" statistic. Indeed, if there were 75 birds for every person on earth, the total population of birds on the planet would be about 555 Billion, or nearly twice the number stated in the film. Additionally, if she is basing her narrative statistics on reduced human and bird populations (because so many people AND birds were exterminated in the first and second waves), HOW would she know that? The first wave knocked out electronic communications, including the Internet.
Other mistake: The kids are "sneaking" into an enemy area but the lights on their helmets and lights inside the helo are on. (01:11:00)
Other mistake: When Cassie runs from Evan's house, she trips over a wire, setting off an alarm. The wire is visible still strung in the shot after that. Evan comes running and simply walks right trough the same wire without jumping over it. (00:54:00 - 00:55:00)
Continuity mistake: After Cassie has been shot in her leg she drops the machine gun, then hides under a car and the machine gun moves between shots.
Continuity mistake: While Col. Vosch talks with Cassie and her family at the camp the sun changes between shots.