The woman talking to John Mulaney et les kids (2019) in "Pay Attention" is his then-wife, Annamarie Tendler-Mulaney.
Jake Gyllenhaal performed his song "Music Everywhere" live on the show, as opposed to recording the song first and then lip-syncing it while filming.
The chess scene is titled zwischenzug, German for intermediate move. It describes when a player delays an expected move in favor of an aggressive move the opponent must answer, which then better allows the expected move. It reflects the nimble and aggressive questions and answers of the scene.
Lexi wears a cast on her right wrist through whole show.