Little Ricky's doctor was Dr. Eugene Gettelman. In real life, he was Lucille Ball's pediatrician for her children. He died 3/14/09 at the age of 100. "Call Dr. Gettelman" in this episode is a tribute to him.
Lucy quotes one sentence from Dr Benjamin Spock's "Baby and Child Care" to support her position that Little Ricky should not go to nursery school: "A good nursery school does not take the place of home." Ricky is suspicious, so he takes the book, repeats what Lucy has read, then continues the quotation: "A good nursery school doesn't take the place of the home; it adds to it. Most children benefit from a good nursery school. It is particularly valuable for the only child, for the child without much chance to play with others, and for the child who lives in a small apartment." Ricky's reading is faithful to the original, except that he leaves out the last part of Spock's advice: ". . . for the child whose mother finds him difficult to manage for any reason." (from the Pocket Book Edition, 1956, p.275)
Little Ricky is called a "3-year-old" several times in this episode, but in the next season's Lucy Gets Homesick in Italy (1956), he is supposed to be celebrating his third birthday.
Replicas of Little Ricky's teddy bear from this episode have been made for merchandising.