Amy (Mary-Louise Parker) tells Josh (Bradley Whitford) a joke about a man who hasn't eaten in 38 days because he was waiting for his mother to call. This joke is also used in Studio 60 on the Sunset Strip (2006), another Aaron Sorkin show, where Harriet Hayes (Sarah Paulson) has trouble remembering the right way to tell the joke.
There is a color-coded calendar in Gayle's fishbowl in C.J.'s office this episode.
The storyline of Josh having once sent someone a dead fish is most likely based on former Chicago Mayor, Rahm Emanuel. When he served on President Clinton's staff, he once sent a pollster a dead fish to show his displeasure with the pollster. As Dee Dee Myers is a story consultant, she most likely knew of this incident involving Emanuel.