The board inexplicably changes in consecutive shots (Around 55:09).
The queen and bishop were shifted one square to the right. It can't be that it shuffled around after a couple moves because the board being played on shows a dark-square bishop and the display board shows a light-square bishop and the quality of the positions are totally different. The display board shows a considerably better position for white.
Borgov looks up as Beth slips away from the adjourned game session. Luchenko and Laev are standing over the chess board. The camera shifts to behind Borgov as he walks to the door and Luchenko and Laev are now seen seated at the board.
When Beth peeps in on Luchenko and Borgov analyzing the adjourned game, Both Luchenko and Laev are standing at the table. Borgov looks up while pouring a drink to see who's at the door. Then the camera angle switches to behind Borgov looking towards the door and now both Laev and Luchenko are seated.
When Beth is on the phone with Benny she is writing left-handed, but she plays and writes her moves right-handed throughout the series.
Moscow tournament was round-robin type. A round-robin tournament is one where everyone plays everyone else. When Beth plays Borgov at the beginning other players should be seen playing their games. Just adjournment Beth/Borgov should play alone.
"There's Nona Gaprindashvili, but she's the female World Champion and has never faced men" - is quoted in the show. Ms. Nona Gaprindashvili has Sued Netflix for the accusations (that she is Russian - She is, in fact, Georgian - and that she has never played with men) and has won the case.
When the tournament director introduces players to the audience, he also says what country they come from. For the Soviet players, instead of the full name of the country, he uses the abbreviation "S-S-R", ("C-C-P" in the Russian alphabet). However, the abbreviation of the full name of the Soviet Union was CCCP - Union of Soviet Socialist Republics (USSR). The tournament director should say "S-S-S-R" ("C-C-C-P").
Townes says the "embassy in Moscow" helped him get a Soviet visa, believing that he would be a distraction for Harman. However, the US embassy in Moscow would want her to win. It would be the Soviet embassy in Washington that would issue the visa, as the Soviet government would want to distract her.
The Kremlin as seen from the restaurant window is much more compact. Its walls would not been seen going on both sides of the Saint Basil's Cathedral to the horizon as seen in a CGI shot.
On the way to Moscow, the Aeroflot stewardess appears wearing a hideous olive-colored apron and matched half-closed headdress. Aeroflon never provided flight attendants with such uniforms. In 1968-1969 it would be a wool skirt suit, navy blue for winter and light gray for summer, and a matching pillbox hat.
During the match against Borgov in 1968, the radio (placed on the roof of a truck) being listened to on the street by Soviet citizens is model VEF 206, which wasn't produced until mid-70s.
Benny suggests that Beth go on "The Tonight Show" and "The Phil Donahue Show" to promote chess and the match in Moscow in 1968. But The Phil Donahue show was not nationally syndicated until 1970 and didn't become a national hit until 1974.
As is the case for many films using old cars, you can clearly see many cars have modern radial tires.
At 34:30, the viewer sees Beth in the dining hall of her hotel with a commanding view of the Kremlin across the Moscow River through 20-foot tall windows. There are no large hotels like this on the Sofiyskaya Embankment across from the Kremlin.
As Jolene's Corvair drives down the road before pulling into the orphanage, there is a close shot of the rear of the car. The license plate clearly indicates Fayette County, which would be correct for Lexington. However, earlier in "End Game", Jolene noted that she is living and working in Louisville, and that the car came from her boyfriend whom she works with/for in Louisville. With that in mind, the car (and license plate) should be registered in Jefferson County, not Fayette County.