Continuity mistake: The Villager Rover attacks changes outfits several times between shots. He's wearing a striped sweater that turns into a pink jacket that turns back into the sweater, etc.
Revealing mistake: Though the Village isn't supposed to have automobiles (only the little "golf cart" transports), there are several parked cars visible in the shot of Rover floating down to attack the fleeing Villager.
Visible crew/equipment: In the foot-chase-on-the-beach scene, there are tracks in the sand from the camera crew's truck. They vanish and then reappear when the camera angle changes.
Revealing mistake: At one point, Rover rolls past the Village retirement home, but the film in this sequence was for some reason shown in reverse. Smoke from the building's fireplace is flowing back into the chimney instead of coming out.
Revealing mistake: When Number 6 first enters the bedroom, the light that hangs from the ceiling is moving as though someone has brushed against it. But there's no one else in the room.
Continuity mistake: The maid comes back to Number 6's house for the feather duster she left behind. While they talk, the duster changes positions on the table all by itself.
Revealing mistake: Number 6 is supposedly flying the helicopter, trying to escape from the Village. There are shadows from the rotor blades crossing his face as he pilots the aircraft. But look closely at the top of the transparent cockpit bubble over his head: you can see the real copter blades - completely stationary and not moving at all.
Continuity mistake: The unfortunate Village resident suffocated by Rover is wearing sunglasses that disappear between shots.
Revealing mistake: No automobiles are permitted in the Village - ever. Yet in aerial shots, a black car is sitting behind Number 2's residence.
Continuity mistake: Watch the stone boat in the background as Number 6 and Number 2 discuss the oldsters having "every comfort." Between shots, the senior citizens vanish from the boat.
Continuity mistake: Rover drags Number 5 back out of the water to the beach and drops him with his feet pointing toward the recovery vehicle. He starts to get up, but when the shot cuts, he's lying flat again and has changed orientation on the sand, his head now pointing toward the vehicle.
Continuity mistake: The dwarf Butler climbs in to pilot the helicopter - but when the aircraft actually takes off, it's obvious that the pilot is a full-sized person.
Continuity mistake: When Number 6 first wakes up in his new house in the Village, there's an ornately carved wood panel covering the window. When he stands, it has disappeared.
Visible crew/equipment: As Number 6 storms out of Number 2's chamber, the camera dolly is briefly visible moving out of his way at the lower left of the screen.
Continuity mistake: The telephone kiosk Number 6 uses at the beginning changes both its shape and its location between takes. Sometimes it's under an archway: in other shots, it's next to the restaurant instead. And in some shots, the hood above the phone has square/straight edges, while in others, its edges are round.
Visible crew/equipment: When Number 6 first walks into his Village bedroom, a film crew member can be spotted walking past the window.
Continuity mistake: When Number 6 is looking for a map in the Village store, the shopkeeper wears a badge with 19 on it. A few shots later, his number has mysteriously changed itself to 56.
Continuity mistake: Number 6 is looking out his window as the maid runs down the stairs. As he watches her, two tables in his apartment change places with each other between takes. A large table with a statue/sculpture on it switches positions with a smaller table on which his lamp and telephone rest.
Continuity mistake: When Number 6 climbs to the top of the bell tower and looks down at the Village, the beach below him changes remarkably between shots. The sequence was obviously shot at different times of day, as the tide is in during much of the scene, but in several intervening shots, the beach sand is completely exposed.
Continuity mistake: When Number 6 observes the stone boat, the tide appears to change from high to low between shots.
Chosen answer: We were never told. In the series finale [Spoiler alert] Number 6 demands an answer to that question, only to be shown his own reflection.
Jean G