Beth is watching Borgov's game in a peach dress and leaves. In the next scene, she returns to her hotel room in a white sleeveless dress.
The Mexican radio commentator uses "caballero" instead "caballo". "Caballero" is the direct translation of knight but in Spanish the name of the piece is "caballo" (horse).
The scene where Beth and her mom stand on the balcony of their hotel shows the Mexico City's Metropolitan Cathedral in the background. However, given the angle and perspective, they would actually be in the Ayuntamiento de la Ciudad De México, which houses Mexico City's municipal offices. It's not a hotel.