The episode title is a parody of the kind of sensationalist television that Fry claims to prefer (e.g. shows of the genre 'World's Blankiest Blank'), specifically When (Animals) Attack, When Good Pets Go Bad etc. The Simpsons also previously parodied this style of show (When Skirts Fall Off, World's Deadliest Executions, When Buildings Collapse).
The destruction of the world monuments by 'anti-monument laser' is a reference to the 1996 movie Independence Day. The first monument to be destroyed is the White House, in a shot-for-shot recreation of one of the movie's most iconic scenes.
The human fleet's approach to the alien mothership is a shot for shot recreation of the Rebel Alliance's approach to the Death Star in the 1977 film Star Wars: A New Hope.
'9' from 'Into the Wild Green Yonder' appears during the celebration after the Omicronians leave earth.