Burger Fool: In the opening sequence the Satellite crew pretend to run a business like this (while Pearl is incessantly calling his name behind him and demanding to know what is taking so long) in order to drive Dr. Clayton Forrester nuts.
As a bonus, Tom and Crow are wearing name tags of other members of the MST3K crew: Tom's says "Paul" (Chapin), and Crow's says "Mary-Jo" (Pehl).
Driven to Suicide: In the very first host segment, Dr. Forrester tried to strangle himself to get away from Pearl. Later, in a parody of Suspicion, Clayton drinks the poisoned milk himself rather than listen to Pearl whine.
Shout-Out: The poisoned milk scene at the end is lifted from Alfred Hitchcock's film Suspicion.
There are numerous shout-outs to The Lord of the Rings, including the closing sketch where Servo attempts to forge a Ring of Power for Mike. Keep in mind this was several years before the movies came out.
Sick Episode: Pearl is suffering from ailment and making Clayton suffer along with her.
(The opening credits show "John Allen Nelson" in a faux-Old English font) Mike:Relson? What kinda name is Relson? Servo: "Nelson", it's "Nelson". Mike: That's one of the most clearly printed "R"s I've ever seen! (And Deathstalker gets called "Relson" through the rest of the experiment.)
Considering that Mike very well knows what the word "Nelson" should look like, this might be a case of It's Personal.
Take That: The host segments really take apart RenFests.