Visible crew/equipment: When Number 6 first walks into his Village bedroom, a film crew member can be spotted walking past the window.
Revealing mistake: After Number 6 has left the Council Chamber for the first time and is heading home, a white car is seen passing by. (00:09:10)
Continuity mistake: When No.2 is writing on the blackboard, in Question A. The capital letter "F" changes several times between the long shots and close ups. Also in Question B. The position of the first "T" in the word together also shifts position during the same shots, showing that the scene was filmed twice.
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.
Free for All - S1-E4
Continuity mistake: The sequences of Number 6's campaign speech scene were apparently filmed several months apart from each other. The trees behind him change from Springtime bloom to Winter bare and back again continually.
Do Not Forsake Me Oh My Darling - S1-E13
Continuity mistake: When Seltzman is talking to Number 2, there's a chair beside the tea cart with a foot rest, visible in the shots from behind Number 2. But when the camera angle changes to Seltzman's POV, the same chair appears in the shot - without its foot rest.
A. B. and C. - S1-E3
Continuity mistake: During the dance, the bottle of wine on Number 6's table is sitting on the left side. No one touches it, but when he and B come back to the table, the wine has moved itself to the center.
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.
Free for All - S1-E4
Revealing mistake: Stock footage puts Number 6 in two places at once when he grabs the bull-horn and starts shouting at the Villagers to go. There's an inserted shot of the plaza from "Arrival" that includes Number 6 walking through it on his first day in the Village.
Continuity mistake: Watch the Butler standing in the background after the committee exits the meeting room. A very bad edit causes him to jump to a different position (a foot further away than he was before) between shots.
Continuity mistake: The new supervisor holds a clipboard in both hands up near his chest. When the shot cuts, he's abruptly holding it in one hand down at his thigh.
Continuity mistake: At the start of the chess match, a man holding a stick climbs the ladder behind the Queen and settles in to watch. As Number 6 and the Queen converse throughout the game, however, both the ladder and the man have vanished. They both reappear behind the Queen as the game is ending.
Revealing mistake: The "metal" door frame in Number 2's office is bubbling and peeling away from the wall.
Do Not Forsake Me Oh My Darling - S1-E13
Revealing mistake: When No. 6 is putting the 4 slides together to get the location information for Seltzman, as the slides are dropped into the top of the projector, they drop down the screen. However, a projector inverts slides, so they should slide up from the bottom. Also, when the last slide is dropped in, the final letters fade into view and not slide down as would be expected. (00:33:30)
Continuity mistake: When Number 6 observes the stone boat, the tide appears to change from high to low between shots.
Revealing mistake: When Nadia and Number 6 are embracing, many of the reverse-angle shots showing them from behind betray the use of a double for Nadia. Nearly every time the camera angle changes, she is noticeably several inches shorter.
Continuity mistake: When Alison and Number 6 are experimenting with the ESP cards, the number of cards in his hand and the designs on them changes between takes.
Continuity mistake: At the end, Number 6 and the Butler catch a bus near Westminster Bridge in London. The bus that drives up and stops for them has no back platform. But when they board, the style of bus suddenly changes to the more common type with an entrance in the back.
The General - S1-E6
Continuity mistake: At the end, the Professor and Number 12 fall dead on the ramp. Between shots, their positions change.
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