Continuity mistake: In most of the scenes it is quite evident that Jessica has only a thin green dress on; when she meets Box she takes it off and she is nude. Later when she is outside of the dome and walking through the woods, she ducks to avoid some brush and she now has underwear on.
Other mistake: In the first carousel one of the female contestants is obviously pregnant. But in the film babies aren't born from a mother but through artificial means.
Suggested correction: I just watched the scene on YouTube and didn't see anyone who was "obviously pregnant." Who are you referring to?
Revealing mistake: When the dome city starts to blow up, people are running around in a panic. One man in a red outfit jumps off a balcony to the next floor and you can see a modern (1970s) lit exit sign over a doorway behind him. Many of the interior shots for the dome city were filmed in a large shopping mall; that sign must have been missed when they were trying to make it look like the year 2274.
Continuity mistake: As Logan walks up the steps with Jessica, the cut in his shirt and his hair part are on the right side, whereas they are supposed to be on the left.
Continuity mistake: In the ice cave, Logan and Jessica take off their clothes and put on animal skins. When they run out of the storage chamber where they saw the frozen cadavers, they drop the skins and are fully clothed.
Suggested correction: Before that scene, they are shown getting dressed. If you saw this on television, they may have cut the shot because of some brief nudity.
Continuity mistake: When the surgeon dies, Francis grabs Logan's arm but a shot later he is grabbing his chest.
Continuity mistake: The cut on the surgeon's shirt is suddenly reversed a shot later.
Continuity mistake: When the surgeon's face is cut he turns his head to the right. A shot later he faces the left side.
Revealing mistake: At the surgeon, the laser cuts the stretcher (a superimposed red light), but when the lasers go berserk they don't cut anything, revealing they're just lights.
Continuity mistake: When Logan empties his pocket in the scanner, they keep changing positions between shots. (00:21:30)
Continuity mistake: Francis walks towards an identity detector machine where he drops stuffs inside and places his hand. The stuff disappears and reappears between shots.
Continuity mistake: Logan and Francis meet a bleeding man by the steps and Logan walks ahead. A shot later he is next to Francis.
Revealing mistake: When the film starts Logan and Francis chase a runner who stands by a column, the squibs used to allow for the sparks and FX are visible.
Continuity mistake: When Logan talks to Francis about his baby, Logan's hand swaps between being by his side to being on the glass. (00:03:08)
Revealing mistake: In the opening scene at the nursery, a flesh colored clip is visible on the baby's hand. It is holding the white crystal to the center of his palm. (00:02:48)
Visible crew/equipment: Right after the Carousel segment, a red-clad man is running because his life-gauge says he's 30. He runs through a semi-open corridor that has dark tan bricks. A moment after he passes through the area, and turns back to see Logan aiming at him you can see a spark emitting device has been colored the same as the bricks, but noticeable. It is a special effect to complete the scene.