Continuity mistake: During the meeting between people and the Government the stuff on the table keeps moving between shots: the bowls that the guy slides trough the table, the tray with a glass bottle, and the book in front of Roy.
Continuity mistake: When Roy wakes up his wife to tell her about the UFOs, the pink tissue paper in the box behind swaps from lying flat to standing up between shots.
Continuity mistake: In Sonora, the scientist walks towards some Mexican officers standing by a stone wall, and a wooden fence is ahead. A frame later, they're standing next to an iron spring and a wicker basket that have appeared out of nowhere.
Continuity mistake: Roy meets Jillian and then walks away to look after Barry. In the next shots with the kid, Roy's hair is longer and messed up.
Continuity mistake: The mess next to the fridge differs between shots, the egg box flips over for example.
Continuity mistake: When Ronnie rescues Roy from the bathtub, a rope next to him disappears between one frame and the other.
Continuity mistake: When Roy is driving to Devil's Tower he is about to crash against two cars. From the opposite angle the cars are different.
Continuity mistake: In India, Claude asks the Guru where the sounds came from, while a huge crowd walks along the desert. When a man in blue addresses the crowd to ask them, the crowd on the right side is gone, and the ones on the left aren't walking but standing perfectly formed like an army.
Continuity mistake: In Jillian's house, when the aliens launch the floor vent it lies on the right side, half a meter away from the hole. A frame later it's lying skewed on the hole. Should the aliens have moved it, a sound would've been heard.
Continuity mistake: When Roy is shoveling dirt through the window he leaves his shovel on the wheelbarrow. When he comes back three seconds later, the shovel is in a different position.
Continuity mistake: When Roy starts throwing plants in the window, the glass gets smashed. Then they open it. When Roy closes the window after he climbs in, it is no longer smashed.
Continuity mistake: Roy's first encounter is with a ship that comes up behind, goes overhead and briefly reappears in front. When it's glimpsed passing above, it's moving towards him as if it came from ahead.
Continuity mistake: Barry is leaving his house, going towards the trees. Jillian looks out her upstairs window and Barry as well as the immediate area surrounding him are drenched in bright direct light, as if from a spotlight mounted on the side of the house. However, from an outside angle of the scene he is not bathed in light, and neither is the area he is in.
Continuity mistake: The pattern of shaving cream on Roy's face changes during the scene in which he gets fired.
Continuity mistake: When Barry is taken from the house, just before that happens we see a grate get blown out of the floor and it lands on its side. In the next scene the grate is back in the hole, but at an impossible angle, even if it fell in.
Continuity mistake: When Jillian's kitchen goes wild, the heater's lids fly off and reveal some red foam which ends up breaking and making a hole. A frame later from a new angle the foam is fixed.
Continuity mistake: Roy is about to run Barry over with his truck and stops on the side of the road. The position of the papers on the dashboard changes between shots.
Continuity mistake: Ronnie says "It's one of those things" and Roy follows her with his hand filled with shaving foam. In the next angle the amount of foam on the right hand is bigger.
Continuity mistake: When Roy and Jillian meet, the redness on Roy's face keeps darkening or lightening randomly between shots.
Continuity mistake: When Barry walks outside the house and his mother calls him, from the shots inside she is surrounded by curtains moved by strong air. From the opposite angle the curtains are gone.
Chosen answer: I own the original (not special edition) DVD and I can always freeze the film and point out to people where the alien is and they see it too, but I can never see it when it's on TV or on my friends VHS copy, maybe it's just a 'gift' for the DVD owners?