Beth and her adoptive mother are seen traveling first in a Boeing 707 and then in a Boeing 727. The cabin scenes though are filmed in a Sud Aviation Caravelle clearly identified by the triangular windows.
When the interviewer asks Beth how she learned to play chess, she replies that that Mr. Shaibel taught her when she was eight, however she didn't meet him until she was orphaned at nine years old.
In her game against Benny Watts, Beth plays 3.d4 as the third move of the game. After she loses the game, in the final position there is a white pawn on d2. It is technically impossible for the pawn to be there after it was moved in the opening.
Beth mentions that her rating is "over 1800". In the Elo rating system, this is not an especially high rating, reflecting a club-level player rather than an expert. Having won the Kentucky State Championship and at least three other strong tournaments and defeated several masters, Beth's Elo rating would have been well over 2200.
D.L. Townes mentions that he was a writer for the Herald-Leader. While the present (2020) daily paper has that masthead, at the time of the Las Vegas Open in 1966 there were two daily papers in Lexington, KY; the morning Herald and the afternoon Leader.
In her second game it's visible that Beth is checkmate (black Queen covers the Rook to checkmate).
When Beth and Vasiliy are taking pictures in the hotel room he spools the film and it makes the sound of being out of film. The Rolleiflex that he is using would also lock the spooling arm in place when spooled enough, proving it's out of film.
After Benny tells Beth of the fatal flaw that could've led to her defeat against Harry Beltik, Beth angrily strides over to a nearby chessboard. As she approaches it, it's clear that the board is set up to begin a game. But in the next shot, as she sits down, the pieces are already set in various places as though it was abandoned after a game.
Actually Beth sat there to revisit her earlier game and the scene was cut to show that Beth had in fact rearranged the pieces to think about her move.
While on an airplane to a tournament, Beth is practicing openings on a travel chess board. She moves a white bishop from a green square to a red square, a space it is not possible for that bishop to occupy. She then moves a knight as if it were a pawn twice. However, she is just rearranging the pieces instead of making actual moves.
On a number of occasions in the series, high-ranked payers are checkmated. This almost never occurs in competitive matches, as players usually resign well before they can be checkmated.
At the beginning Alma and Beth enter the hotel room in Cincinnati. Alma turns on the TV and immediately the screen shows a broadcast before she turns it off again. This would not have been possible with a 1960s cathode-ray tube television as it would have taken quite some time to display an image.
Beth and Alma are shown flying to Houston on a Boeing 727 on Christmas Day, 1963. The 727 did not begin passenger service until Feb. 1, 1964.