"Fat Man" and "Little Boy" are the code names of the atomic bombs dropped on Hiroshima and Nagasaki in 1945 at the end of World War II.
Matt Groening actually registered the domain www.nuclear-secrets.com (the website Homer visits) before this episode aired, but did not create a website.
A shirt Moe asks Bart about is one of Calvin peeing on Hobbes; he then asks what Calvin is peeing on if not on Hobbes. This is a reference to how the protagonist of Bill Watterson "Calvin and Hobbes" comic strip was for a time depicted as urinating on certain brands' names by rival companies before it was ruled illegal as it never had Watterson's approval.
The nature documentary Homer watches about lions is presented by recurring character Declan Desmond (Eric Idle).
Goose Gladwell's costume is modeled on that of Willy Wonka.