This is the second appearance of a Robot Chicken (2001) animation in the couch gag. The first one was in Season 24's The Fabulous Faker Boy (2013).
Barney says to Homer "You're playing like Polugayevski at Mar del Plata". The 1982 Mar del Plata (Argentina) chess tournament was won by Jan Timman, but Polugayevski (who was 5th) achieved the title of Grandmaster.
Magnus Carlsen (guest on this episode) is the fourth younger player ever to be Grandmaster (at the age of 13 years, 4 months, 27 days).
When Homer is searching for the stolen sailboat painting he walks through an animated set of South Park therefore making it the second time the series is referenced or seen on the show in an earlier episode Simpsons characters appear in a South Park like form.
Moe's Tavern still has a payphone. It can be seen in the background.
WILHELM SCREAM: In Bart's video game.