According to the mini commentary, Randy drinking while driving and then later urinating into a bottle plays into a similar instance that Trey Parker's father did while on a road trip.
At 13:58, when Randy is trying to drive under the influence again, you can see reflection of an alien in the window of his car.
The leader at the front stand of Randy's Alcoholics Anonymous group is the same guy who was in charge of the weight loss camp in Fat Camp (2000).
Alcoholism was actually declared a disease by the American Medical Association in 1956.
In 1991, it was further dual-classified by the Internal Classification of Diseases under the psychiatric and medical sections (this does not, however, mean Randy is a legitimate alcoholic).
The original air date in 2005 was the the day before the Feast of the Immaculate Conception.