During the Muppet portion of Cliff's dream, Gonzo announces that Cliff will be making the first delivery of a Koozbanian ever seen on television, but Kermit the Frog did a news report about the first Koozbanian birth on The Muppet Show back in 1976.
Gonzo (on stage): Good evening ladies and gentleman...and other things.
Olivia: I don't have any friends. I live here with a bunch of old people.
Waldorf: He doesn't look like he can deliver a baby!
Statler: He doesn't look like he can deliver a pizza!
The reason for Bill Cosby's substitution for the old man in the theater was that due to Jim Henson's sudden death, there was no one to play his role of Waldorf, the elderly gentleman who usually sits next to Statler on The Muppet Show. Cosby is made up to look like Waldorf for the sketch.
The man in the operating theater who yelled, "He doesn't look like HE CAN DELIVER a BABY!!!!!!" was Bill Cosby dressed up.
The people at the table with Olivia in the black and white scene are all members of the show's crew: co-executive producer John Markus, supervising producers Carmen Finestra and Gary Kott, producer Terri Guarnieri, co-producer Matt Robinson, story editor Ehrich Van Lowe and writer Lore Kimbrough.
According to the production code, this episode was produced for the fifth season. However, it may not have been completed until season six, as Raven-Symone appears in the episode and Clair makes reference to Cliff's dream about the pregnant men, which occurred in a sixth season episode. Lisa Bonet (who also appears) was absent for most of season five.
The monsters featured are from Jim Henson's Productions and Sesame Street. Both series were filmed in the same building. When Jim Henson died, the episode was dedicated to his memory.
The nightmare Cliff was having has a bunch of food and characters talking to Cliff. This is like the children's TV show on PBS called Sesame Street created by Jim Henson where a bunch of characters teach children reading, writing, and numbers. The show premiered in 1969.
Cliff: "'Cause there's no place like home."
This is a famous line from "Wizard of Oz" which Dorothy says when she and Toto return to Kansas.