Hayley is sculpting the mountain from "Close Encounters of the Third Kind."
A parody of the film "Akeelah and the Bee" (2006) which also features an Asian-Anerican character
The sword fight between Francine and Akiko's mother is similar to fight sequences in "Crouching Tiger, Hidden Dragon".
When Hiko commands Toshi and Akiko to "show them fun" to Steve and Francine, they play a string version of Dexys Midnight Runner's hit song "Come on Eileen," which has made appearances elsewhere throughout the series.
When Francine is complaining about Hiko to Greg and Terry, their daughter Libby comes in briefly wearing a fencing outfit and greets her fathers in French. Francine wonders why Libby is still speaking in "baby talk" before being corrected by Greg. This makes no sense, however, as Francine learned French back in Season 4, and has spoken the language on several other occasions.