When Carter says he going to shoot a lion with some scumbag dentist, he's referring to the Minnesota dentist Walter Palmer who in Zimbabwe in 2015 killed a beloved lion named Cecil, and paid $50,000 (USD) for the privilege.
When they show the cutaway of Carter rearranging the furniture, he is doing Jamiroquai's music video "Virtual Insanity" from the 1990s.
There is a cutaway scene featuring Neil deGrasse Tyson in the Spaceship of the Imagination from the series Cosmos: A Spacetime Odyssey. Seth MacFarlane is one of the executive producers on Cosmos: A Spacetime Odyssey and is a personal friend of Neil deGrasse Tyson.
When Peter enters East Bola the sign reads E.Bola a reference to the virus of the same name.
The title is a reference to the musical "Damn Yankees".