This episode features the main character playing simultaneous games of blitz chess against three opponents in a basement apartment. As the last game of that scene concludes, the camera lingers over the final position revealing it to be the very famous game Paul Morphy vs. Duke Karl / Count Isouard (1858). That game features numerous piece sacrifices by Morphy to achieve a superior position, with a final Rook+Bishop combination to deliver checkmate.
The role of Ed Spencer, director of the Kentucky State Championship in this episode, is played by Bruce Pandolfini, one of the most famous chess teachers, himself a former national master, and the chief technical advisor on the chess games for The Queen's Gambit. He had also acted as chess consultant to Walter Tevis on the original novel. Pandolfini taught the actors, among other things, how professional players move their pieces.
Benny advises Beth to play the Sicilian Defense against Borgov in Paris. In fact, the opening in the game they play is a Sicialian Defense: Open, Scheveningen, Sozin, Flank Variation (ICO B87).
The final combination in the last blitz game in New York between Beth and Benny is from the famous game Morphy vs. Duke of Brunswick, 1858; certainly an inside joke from Kasparov and Pandolfini.
The song Beth is dancing to in her underwear is 'Venus' from the Dutch band Shocking Blue. In their home country it never reached the number one position in the charts, as opposed to the USA and a lot of other countries, where it did reach a number one position. In the Netherlands it's a real evergreen. The song is covered a lot of times over the years. The British girl band Bananarama covered the song in 1986 and also reached a number one position in the USA.