The scene when the taxi driver unsuccessfully tried to get away, refusing to drive Homer to the airport for less than $20, is a reference to the "Tank Man," who stepped in front of a tank during the 1989 Tiananmen Square Uprising.
The episode of The Itchy and Scratchy Show: "Ain't I A Stinger" is a reference to Bugs Bunny's quote: "Ain't I A Stinker".
The picture of the dog on the chair at the end of the episode is a reference to 2010 Nobel Peace Prize winner Liu Xiaobo.
Thicker than Waters is largely based on late-'80s sitcom Growing Pains. Even the title is a slight nod to Alan Thicke, who played Dr. Jason Seaver on Growing Pains. Patrick Waters has a similar profession to Jason Seaver, while the mother resembles Joanna Kerns, aka Maggie Seaver.
Upscalien in the House seems to be based on the sitcom The Fresh Prince of Bel Air. The title sequence itself seems to be very similar to the opening sequence.
I Lost Lucy is likely a pun of I Love Lucy.
The Voiceover Years is likely a pun of The Wonder Years.
Sam Waters (Patrick's son) is wearing a uniform similar to the '80s Houston Astros.
When one of the Chinese agents hold a teddy bear in front of Bart in revenge for ripping them off, Bart questions the use of a teddy bear as a weapon. The agent responds that it was made in China and rips off its head to reveal a spike. The other agents take out similar objects. This is a reference to the 2007 Chinese export recalls.
The episode's name is a reference to God the Father.