The title is a reference to the Jim Carrey film of the same name.
The "comedy dog" puppet that the obedience school drill sergeant refers to is Triumph, the insult comic dog.
The scene of Brian in the chair is a parody of A Clockwork Orange, complete with the "Ode to Joy" from Beethoven's 9th Symphony.
The "Don't Get Shot by a Bullet" ad is a parody of the "Let's All Go to the Lobby" movie ad from the 1950s. The song references such shootings such as one in Aurora, CO in 2012 that killed 12 people and left 20 injured.
Neil holding a boombox out Chris' window is a parody of the final scene from Say Anything.
The obedience school drill sergeant refers to The Artist, a 2011 film about a relationship between an aging silent film star and a younger actress in the new "talkies" films.