After the quote from The Wrath of Khan, Kyle says "That was Star Trek again", underlining the fact that South Park often makes Trek references.
Randy's presentation includes a 'disaster' photo of a woman's very odd face. That was the mega-rich socialite Jocelyn Wildenstein. In 1999 she was famous for her excessive cosmetic surgery and for receiving a divorce settlement totalling just over 3.8 billion dollars. The settlement specifically stipulated that none of the money could be used for more cosmetic surgeries.
The statue South Park gives to Randy is a replica of Michelangelo's David with Randy's head.
While Cartman is on the cross over night, the image of a Visitor's face can be see on the moon.
The formulas written by Randy near the end are the same as those written by Herald R. Pinkerton, Nobel Science Prize nominee.