Continuity mistake: After the train wreck, one scene shows the car they came in has a steel or wooden beam/bar stuck into the rear wheel area and debris is piled close to the car - yet when they get in it to escape, the car is clear and they easily pull out of the lot. (00:19:25 - 00:24:35)
Continuity mistake: In the camera store, Joel stands in front and to the left of a Kodak film advertising display. After briefly cutting away, the camera returns to find the display now rotating.
Continuity mistake: When the boys are running through war-zone Lillian, they are shown running quite spaced. A shot later they're running in a clump. (01:26:30)
Continuity mistake: In the bedroom scene, when the camera looks out of the window at Alice, she's wearing a plain blue t-shirt with a denim jacket. After she's climbed in, it has writing on.
Continuity mistake: In the scene when Alice tells Joe not to let Charles blow up his model train, her hair moves from hanging downwards to tucked behind her ear between shots. (00:57:45)
Continuity mistake: When Joe and Alice are talking in his room, there is a book in the background on a desk or such that changes position between shots. Sometimes it is upright and sometimes at an angle.
Continuity mistake: When the kids are gathered to film on the hill with the train crash in the background, Joe grabs the camera to get a closer look, setting up the tripod a couple feet away from Alice. Joe hunches forward to look through the camera. Then the group is shown from behind and Joe isn't hunched forward anymore. Alice is still a couple feet to the right and Cary a couple feet and forward to the right of her. When the camera comes back around to the front of them, Joe is hunched forward again, and Alice & Cary are right next to him. (00:32:00)
Continuity mistake: After the train wreck, all the kids are looking for Alice. When she shows up behind Joe, his fringe swaps between brushed and messy, back and forth. (00:20:15)
Continuity mistake: Jack stares at an army truck and turns his head to the left. From the opposite angle, his head is still and he is turning it again.
Continuity mistake: Jor's hair changes scene to scene from short to long.
Continuity mistake: During the wake, a red/burgundy car is parked along the curb after the Lambs' driveway sometimes but not others. It is first seen at 00:01:30 immediately past the driveway but is not there when a light-colored (white, grey, light blue?) car is parked along the curb two or three houses down. When the sheriff's car has backed out of the driveway and onto the road, the red car is suddenly back again, a little way past the driveway entrance but before the light-colored car. The red car could not have just got to that spot because Mr. Lamb backing out of the driveway would have blocked it from getting there plus the road may have been slippery/icy (where drivers need to go slowly). (00:03:43)
Continuity mistake: There is no center line dividing the lanes on the street where the Lambs live, but the street is divided by a double-yellow line when Mr. Lamb puts Mr. Dainard into the sheriff's car. (00:02:43 - 00:03:43)
Continuity mistake: When Joe goes to Alice' porch and trying to convince her to come back to film more of the movie, her arms are down at her side in her close ups. But from the side shot, her right arm is extended up some and holding onto the chain of the swing. (00:29:57)
Continuity mistake: After the train crash and Joe is back home, his dad wakes him up and he is facing off to the side as he opens his eyes and starts to lift his head. It cuts to a different angle showing the white cube in the foreground and suddenly Joe is looking up fully at his dad. (00:26:40)
Suggested correction: I watched a few times and saw a rather good, smooth series of movements - they did not look awkward at all. I did not see what you saw, which leads me to suspect corrections were made or your DVD player "skipped."
Maybe one more person will check his/her copy.
A small hiccup in the stream might be an even better explanation for the discrepancy - in which case "I saw what you didn't see" would be more accurate than "I didn't see what you saw."
Continuity mistake: While the boys are looking at Dr. Woodward in his smashed truck, there's a quick close up of Joe's face before Charlies asks Cary about the teacher taking his electronic football. Joe's face is mostly in shadow on his right half with his left half in the light from fire. When it cuts to a different angle showing Charles talking, suddenly his whole face is lit up. (00:22:30)
Continuity mistake: Once they find the smashed truck with Dr. Woodward in it, they are standing in a way that Preston and Charles are almost shoulder to shoulder but with Martin between them slightly behind them. When the shot cuts, suddenly Charlies is in front of Martin with Preston behind Martin. (00:22:20)
Continuity mistake: At the train stop before they start filming, Joe is about to put makeup on Alice and asks her "Do you mind?" In the view of his face, the wind is blowing Alice's hair and several strands are over her cheek and blowing into her face. When it cuts to an angle showing Alice's face, it is clear of hair with it blowing back. (00:12:25)
Continuity mistake: When the kids break into the school and discover the footage of Dr. Woodward and the other scientists, they break a window on the classroom door. The glass is almost completely removed from the frame but once the military arrive and take the kids away, there is suddenly more glass in the frame. (01:14:50 - 01:17:25)