When Shawn mentions at the beginning of the episode that somebody in Washington invented silent window shades, he is referring to Nadine, the woman who wore an eyepatch on the show "Twin Peaks" and was attempting to patent silent window shades on the early episodes of that show, which was set in the state of Washington.
Star James Roday Rodriguez, a huge "Twin Peaks" fan, co-wrote this episode as a tribute to that show.
In a nod to Twin Peaks, Paula's friend, Jack, is blind in one eye making him a One Eyed Jack. The name of the Canadian casino and brothel from the show.
Several of the guest stars who starred in "Twin Peaks" (1989) are playing parodies of characters from their original show, right down to their names. Most notably, the sheriff's name is Andrew Jackson, a presidential nod to Twin Peaks sheriff Harry S. Truman, and the character credited as The Wood Woman is the same actress who portrayed the Log Lady in Twin Peaks. And to put a Psych-esque pop culture spin on things, Sheriff Jackson's son is named Randy Jackson, after the music exec/American Idol judge.
Paula Merral, the name of the principal victim in this episode, is an anagram of Laura Palmer, the name of the principal victim in Twin Peaks (1990).