Peter's breath fogs up the window in his cell when the shot is looking in, but the fog is never visible when the shot is looking out.
It is mentioned the 29-move game Steinitz-Chigorin 1892, where the final move is Q-B4. There is no such game.
In the second game of the match Cordel is playing Black again. They should alternate colors.
Jim uses a computer to defeat club chess champion Peter Cordel. In 1972, computers were not capable of playing chess at this level of expertise.
As a matter of fact, most gadgets used by the team are purely science fiction and cannot function as portrayed.
Phelps hesitates in the opening moves of the chess game. This is the English Opening (1. c4 Nf6), where 2. Nc3 is the standard reply. The fact that Phelps hesitates on what should be an automatic reply (Phelps wouldn't open with 1. c4 unless he was familiar with the options for both of the standard responses by Black) should have been an immediate tip-off to Cordel that something was amiss.
That is wrong, the English Opening is highly flexible, allowing for various next moves. Phelps is correct to hesitate.
When Sandy is being held at gun point in the limo at the end of the show, the man holding the gun is not wearing glasses. When the camera angle shifts to a viewpoint from behind the gunman he is shown wearing glasses. When the viewpoint returns to showing the front of the gunman he is again no longer wearing glasses.
The newspaper article about the "Chess Club Murder" is long but only the first two paragraphs are concerned about the crime; the rest is from other news.