Couple of times a single game is referred to as a "match".
A match is a series of games, as in tennis.
Benny advises Beth that they never announce "check" in first class tournaments, and that it is not normal to resign by toppling the king. An experienced player like her would be well aware of tournament etiquette.
In the last game of the simultaneous blitz chess scene, the king is on b1 instead on c1.
When Benny Watts pays the $10 bet to Beth, he pays her with three bills. No combination of three bills will come to $10. However, Beth had bet $10 on each of the blitz chess games against Benny, Arthur, and Hilton, so each round of wins would net Beth $30 of Benny's money.
Beth hits her head and blacks out while watching TV, but when she comes to, the TV is turned off.
This episode features a montage of Beth dancing to the song "Venus" by the Shocking Blue. This song was released in July of 1969, two years after this scene supposedly took place.
(7:55) In 1967, Beth can be seen outside a Saks Fifth Avenue store with a logo that was not implemented until 1973.
As Beth is waking up at 5:42, you can see her wig cap on her forehead.
Cleo, who is French, reaches for the word ("how you say?") "vagabond", which is a loanword from French with the same meaning in both languages.