Continuity mistake: While Alex is talking with his parents before the trip, there is a small object besides the switch that disappears between shots.
Continuity mistake: Before Alex and his friends enter the airport there is lady in white that crosses the door at least 3 times.
Other mistake: When Carter is basically trying to kill himself with the remaining "survivors" in his car, Billy makes a comment saying that when he saw Alex leaving Mrs. Lewton's place, Alex's shoe prints were in her blood and his prints were on the knife. All good and fine but there's just one thing that doesn't make much sense. Her house blew up right after he ran out, so could anyone still pull off any prints from the knife that killed her, and see footprints by her body? Wouldn't that evidence be gone in the explosion?
Suggested correction: Not necessarily. An explosion doesn't mean that everything around it is incinerated. Depending on where the explosion originated, certain items can be shielded from the blast/fire by larger objects, and I believe they mentioned that the fire caramelized the bloody footprints.
Continuity mistake: When you first see Carter's car you can see that is says "SS" on the front. Then when he almost hits Billy at the school it doesn't say it. Then when he is on the train tracks it says "SS" again.
Revealing mistake: When Alex is running through the woods and is sliding down the hill, just before he stops himself from being impaled by some branches, you can hear someway say "Look out." It can't be the agents following as they're too far away.
Factual error: When Ms. Lewton takes out her mother's favorite record album, the label is obviously a fake. None of John Denver's albums had his name written that large on the label.
Suggested correction: I think this is for two reasons: i) Copyright. ii) To show to the audience she is going to die by making the song obvious to them.