ARPANET (Advanced Research Projects Agency Network) is the military and academic forerunner of the modern-day Internet. It was created during the Cold War by the U.S. Military as a way of maintaining control over subordinate commands in the event of a nuclear war. After the Cold War ended it was declassified and opened up to public use.
As Philip shows Henry an ad for a 1982 Chevy Camaro Z28, he sings a snippet from the Eddie Rabbit song "Drivin' My Life Away".
Anastasio "Tachito" Somoza Debayle was a Nicaraguan dictator and officially the President of Nicaragua from 1 May 1967 to 1 May 1972 and from 1 December 1974 to 17 July 1979. As head of the National Guard, he was de facto ruler of the country between 1972 and 1974 even during the period when he was not the de jure ruler. After being overthrown in an insurrection in 1979 led by the Sandinista National Liberation Front (FSLN), Somoza fled Nicaragua. Power was ceded to the Junta of National Reconstruction. He was assassinated in 1980 while in exile in Paraguay.
The Intellivision game Henry is playing at the Tanners' is Astrosmash.
As Professor Rosebloom explains how the ARPANET works, he uses an analogy that references WW2 Japanese emperor Hirohito.