Continuity mistake: Number 39 is writing notes on the word association test in her notebook. When the shot cuts to a close-up, however, the notebook disappears from her hands. It's back a short time later.
Audio problem: During a fight with Number 6, one of the Village keepers falls from the bell tower. His fall terminates in the sound effect of a loud splash - but the bell tower isn't anywhere near any water.
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.
Continuity mistake: Rover herds the boat back to the beach, and several people who were aboard minutes before (some of them unconscious) have somehow disappeared from its decks.
Continuity mistake: Number 6 is taking notes on the Village inhabitants, trying to determine which of them are prisoners and which are keepers. Next to the pond, he's observing Number 62. But on his notepad, he crosses out Number 8.
Continuity mistake: At the end of the chess match, the player wearing blue comes down off his platform, descending the ladder and walking onto the field. In the very next shot, as his opponent approaches Number 6, the man in blue is in the background, once again coming down the same ladder. He didn't have time to climb it again.
Continuity mistake: In the opening shots, the Village center is shown without the giant chessboard set up. In the very next shot, it is suddenly fully laid out on the green.
Continuity mistake: When the command "Knight to Queen's Bishop Three" is given, it's not a knight that moves, but a pawn. In the next long shot, though, Queen's Bishop Three isn't occupied by anyone, pawn or otherwise.
Factual error: Several of the chess moves called out over the loudspeaker are not possible with the players in their current positions. The Queen, for instance, is ordered to King three while in her starting position (can't be done). The "Knight to Knight's Bishop three" move is also impossible. When she is free to move to King three, though, the Queen goes there twice - without moving anywhere else in between.
Continuity mistake: When Number 6 is setting up his antenna, there's a woman on the beach in the background in a blue bathing suit. Between takes, her beach umbrella disappears.
Visible crew/equipment: When Number 6 is listening to classical music in the listening booth, each time he puts his head into the booth (after switching records) there is a specific shot behind his shoulder where you can see the heads of two crew members reflected in the glass of the listening booth. This happens 3 times and is very visible on Blu-ray. (00:10:33)
Revealing mistake: After Number 14 convinces Number 2 to let him deal with Number 6 both of them leave 2's office. As they do, you can see the "metal" on the doorframe has started to bubble. (00:30:57)
Continuity mistake: When Number 6 writes the coded message he uses black ink, after Number 2 intercepts the message it changes to blue ink. (00:37:24 - 00:38:30)
Continuity mistake: When Number 2 is shouting at Number 14, calling him a traitor, Number 2's long strands of hair are flying all over his head. In the very next shot, though, his hair has nicely combed itself and he's well-groomed again.
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: Number 6 points the mirror out to sea and tries to send a signal. But when we see him from the POV of the security camera, he's pointing the signal mirror toward the Village instead. When the shot cuts back to him on the beach, the buildings are again behind him and he's facing seaward again.
Continuity mistake: During their kosho match, Number 6 ends up dangling Number 14 over the water. In the first shot, he's holding the man with his left hand. In the next, he's using his right hand.
Continuity mistake: Just before the fight begins on the roadway, Number 6, in full shot, steps off the grass and onto the road. But the next close-up of him shows him on the grass again.
Continuity mistake: Between the time the coded note is tied to the pigeon and the time it is intercepted and handed to Number 2, the handwriting on it changes completely.
Continuity mistake: When he's standing against the wall of the kosho chamber, Number 6 is holding onto the rail, but when the camera reverses angles, he isn't. This goes back and forth several times.
Chosen answer: We're led to believe Rover is some kind of robot in the series. According to books on the show, Patrick McGoohan was looking for an unusual guardian for the Village, looked up at the sky, and saw a weather balloon, which was what Rover was.
Captain Defenestrator