The tape scene where Jim Phelps receives his taped instructions is re-used from Trek (1967). The scene takes place in a telephone booth, and to obtain the photograph accompanying the tape recording, Phelps (Peter Graves) unlocks the coin box to remove a small, folded envelope containing the photo of their opponent. The photo that Phelps supposedly looks at is much larger than the small envelope he removes from the coin box but has no visible creases. (The contents of the envelope in the earlier episode was a small folded news article.)
When Rollin plays the chess match that gets him into the finals, his opponent's name that is displayed on the front of their table does not match the name that is shown on the blackboard with the pairings written it.
The last number in the combination to the vault is established as 15, but when the desk clerk opens the vault to put in Cinnamon's "jewels", he stops at 2 for the last number. When closing the vault in front of the Captain after the gold arrives, the dial is on 88.
When Barney fakes his attack he grabs his right shoulder, but when he is on the ground and Jim approaches, Barney is clutching his left shoulder.
In the scene where Groat is engaged in his final game against the computer in the hotel room, there are three shots depicting the checkmate. Notably, these shots show distinct board positions.
The show portrayed grandmaster chess in an unrealistic manner. The top computers of that era couldn't beat a grandmaster. Phelps scored each player's piece move move as a separate numbered move; in real chess, one numbered move would consist of a piece move by each side. In grandmaster tournaments, one game is played a day, not the several games in the show. Many of the moves made by the players in the games were rank mistakes that a grandmaster would never make. Players never give checkmate in top level chess. Players resign before checkmate is given.
Barney says that the computer will make the time lock's clock run 20 times normal speed. But the timer on the clock showed a little more than three "minutes" going by every second, which would be about 200 times normal speed. If it was running at 20 times normal speed, it would take three seconds for each "minute" to go by.
Shots of Jim holding the mission briefing photo are static photo composites. There are dark lines around the thumbs where the mission photo was matted into the shot.
In the game deciding the championship, Groat issues checkmate by playing Qxg2 (QxKNP) on the board, with Rollin's king on the h1 square, but the board on the wall then is updated by the referee to indicate that mate was given by the move Qe1 (Q-K8), with Rollin's king on the g1 (KN) square and other pieces also in obviously different places than shown on the board on the table between by the players.
When Groat greets Rollin for the first time, Rollin pauses to turn up the hearing aid volume for his left ear, but he could have heard Groat just fine with his right ear.
When Jim reads Barney's temperature, he gives it as 104.2 degrees. However, in Europe, they use the Celsius scale and he should have said Barney's temperature was 40 degrees.
The team records and communicates chess moves in descriptive notation (P-K4 or "Pawn to King Four"). By the late 1960s, most countries had switched to algebraic notation (e4). While the United States lagged behind the rest of the world in adopting this method, the team has been shown to internalize any number of aspects of another country's culture, so it seems odd that they did not learn to use the algebraic method.