One of the stalls at the CIA fair holds the game "WMD Hunt". This is a reference to the hunt for WMDs in Iraq, a main justification for the 2003 Invasion of Iraq and the perceived unfairness of carnival games. No contestant is able to find a WMD.
Dick's quote "I got the stapler!" is a subtle joke: Dick is voiced by actor Stephen Root, who played Milton in the film Office Space, a character who is obsessed about his missing stapler.
Stan refers to Hayley as "Squeaky Fromme". This is a reference to Lynette Fromme, former member of the Charles Manson "family" who attempted to assassinate President Gerald Ford in September 1975.
The scene where Stan is trying to make Jeff more assertive by telling him a banana is an apple is a reference to the Red Dwarf episode "Camille", when Lister tries to teach Kryten to lie. It is also reminiscent of the famous 2+2 = 5 torture scene in George Orwell's Nineteen Eighty-Four.
The scene where Stan and Bullock are trying to hunt Jeff is a reference to the story The Most Dangerous Game.
The name and logo of the TV network where Bullock is about to announce Stan's promotion is C-Spin, a spoof off of the real network C-Span, including a portmanteau with spin.
When Jeff offers to perform "a blistering flute solo", this is a reference to hard rock band Jethro Tull, whose lead singer, Ian Anderson is known for playing a flute.