Jason Sudeikis and Brendan Hunt used to live in Amsterdam in 1999-2004 where they used to perform in a local comedy club, called Boom Chicago. They even said that this is where they came up with the idea for Ted Lasso and that the show would not exist without Amsterdam.
Ted's "vision" pays homage to "Donald in Mathmagic Land."
The song playing while Jamie teaches Roy to ride a bike ("Raindrops Keep Fallin' On My Head") is the same song that plays during the bike riding scene in 'Butch Cassidy and the Sundance Kid'.
The episode includes a couple of nods to Pulp Fiction. They both include discussion of foot massage technique. When Ted walks into Yankee Doodle Burger Barn, Ricky Nelson's "Waitin' in School" plays, the same song that can be heard when Vince and Mia walk into Jack Rabbit Slim's (a place similarly built on kitschy classic Americana). Pulp Fiction was partly written by Quentin Tarantino during a stay in Amsterdam, and the city is mentioned in two scenes in the movie (including the Jack Rabbit Slim's scene).
The spot where Colin and Trent hang out is the Homomonument, a memorial to gay victims of the Nazi occupation of the Netherlands. Opened on 5 September 1987, it is shaped like a pink triangle in reference to the symbol gay people were forced to wear during the occupation. (It also foreshadows Ted's triangle idea.)