The sketch is a parody of the PBS program, Masterpiece Theater, hosted by Alistair Cooke.
Here is a guide for various Monsterpiece theater segments:
"Me, Claudius" Several monsters fight over which one is claudius.
"The Old Man and The C" Grover is playing an old man on a row boat, which is on a giant letter C.
"The Sound of Music" Grover is sitting on a hill, which moves to the sound of music.
"The Taming of The Shoe" Grover is accompanied by a talking shoe.
"The 39 Stairs" Grover climbs 39 stairs to see what is at the top, and ends up being dissapointed with the results.
"One Flew over The Cukoos Nest" The number one keeps flying over the wrong things.
"Gone With The Wind" Kermit and a girl are in a windy room.
"Guys And Dolls" Herry Monster sings about how he likes to play with dolls, and Ruby sings about how sh likes to play with trucks.
"The King And I" Grover plays a king who dances with the letter I.
"Waiting For Elmo"
"Fiddler On The Roof"
"Dances With Wolves" A pig dances with a wolf.
"Hamlet" Mel Gibson plays Hamlet, who keeps repeating "words, words, words", but Elmo can't read, so he only looks at "pictures, pictures, pictures".
"12 Angry Men"
"Monster in a Box" A small monster does anything wrong with a box.