The "ungrateful gargoyle" that Professor Farnsworth is searching for is named Pazuzu, which is the name of a Mesopotamian demon who was considered the King of evil air spirits. It is the name of the demon who possessed Regan ('Linda Blair') in the The Exorcist (1973).
Youthicizer Heather says "botulisn toxin tightens and tones the facial muscles". Actually, botulinum toxin (BTX) causes flaccid paralysis of muscles. Botox facial treatment famously paralyzes muscles so much that you can not display any facial emotion. The bulgy can is accurate; throughout most of the 20th Century the main source of botulism was improperly canned non-acidic food.
The monster on the cover of the children's book Fry asks Leela to read from is an alien from Star Trek (1966), specifically it is the Gorn Captain Kirk is forced to fight in Arena (1967).
The bacteria that should eat a substance making the professor Farnsworth and his crew younger is a nod to arcade game character Pac-Man. When the bacteria is shown in holographic animation the theme music from the game Pac-Man (1980) can be heard.