When Shawn and Gus are talking to the Coach in his office, Shawn points out a series of players who have things going on in their lives that they're trying to keep secret. The last player he points at (but doesn't mention by name; the Coach fills this in in the next line) is "Dorn (9)", saying he's "probably gay... definitely gay." Roger Dorn, #9, was the name of the character in Major League - La squadra più scassata della lega (1989) played by Corbin Bernsen, who plays "Henry Spencer" on Psych.
Regarding his plans to patch things up with his dad, Shawn says "I'll make it up to him this week. Head over there for dinner, bring him a pouch of Big League Chew, maybe watch a few episodes of 'The Mentalist.'" This is the first in a long line of jokes about "The Mentalist" throughout the series, as both shows revolve around a hyper-observant man helping the police with cases by pretending to be psychic, a premise Psych employed first. The showrunners have repeatedly implied that The Mentalist pirated the idea from Psych, arguably enjoying more success.
The Thunderdome is portrayed by BC Place in Vancouver, BC which is where Psych was filmed. The football field shown was clearly a Canadian Football League field as it is 10 yards longer than an American field and the goal posts are positioned at the front of the endzone instead of the back.
In the laundromat, the lady behind the counter has a picture of Shawn, as Chad from "Psych" (2006) {Lights, Camera... Homicidio (#2.13)}. In the close-up shot of this photo, the picture to the right of Shawn's is that of Andy Berman, writer of that episode, among others.
Shawn also says of football, "It's the only thing my dad and I both like, besides Asian slaw and Harry Hamlin." Shawn's father is played by Corbin Bernsen, who starred with Harry Hamlin on Avvocati a Los Angeles (1986).