Apparently, the All Valley Tournament rule where the defending champion only fights in the finals (as seen in The Karate Kid Part III (1989)) has been abandoned, because Xander, the defending champion, had to work his way through the tournament.
Rocky III (1982) is mentioned. Rocky (1976) and The Karate Kid (1984) had the same director, John G. Avildsen.
During the City Council meeting in All Valley (2018), one of the council members suggests it's time to "shake things up" at the All Valley tournament by changing the traditional red mats with a white fist to blue mats with a gold fist. As the opening tournament prep montage in this episode shows, he gets his wish.
Robby's slicked back hair with the small ponytail looks very much like the villain from The Karate Kid Part III (1989), Terry Silver.