On American TV, this episode was originally rated TV-PG for violence (V). The rating was later changed to TV-14 due to the heavy references to marijuana smoking, along with the violence (Homer getting pecked by crows, a teenage Homer getting bitten in the crotch by a drug dog, Homer bleeding "rainbows" as he shaves himself under the influence, and Mr. Burns bleeding while being used as a marionette).
The title for this episode comes from the movie Weekend at Bernie's (1989), which is also about two guys trying to make people believe their dead employer is still alive.
When this episode first aired in Australia, it was flagged as "Adults Only" and aired at a later time slot then usual. In the U.K. they actually refused to air it for several years due to a fear that it was "Glorifying Drugs". FOX eventually stepped in a censored a lot of Homers Drug use throughout the episode due to the concern, so all subsequent airings had scenes and moments cut out (even in the U.S), regardless the episode is rarely shown on TV.
Homer mentions that, since he has a prescription, he could "walk right up to the President and blow it (Marijuana smoke) in his stupid monkey face..." George W Bush was the President at the time.
The music playing while Marge builds her scarecrow is "If I Only Had a Brain," the Scarecrow's song from 'The Wizard of Oz.'