The last line of the show with which Murphy refers to herself, Eldin, and Avery as "the traditional American family" is likely in reference to comments made in Dan Quayle's real-life speech on family values the summer before, in which he criticized the character of Murphy Brown for her "lifestyle choice" of having a baby without a father.
Eldin: (on being Avery's nanny) The only problem I see is that I have a slightly more feminine side to me than you do, and that might confuse him.
Eldin: What's his middle name?
Murphy: Middle name?
Eldin: He's got to have a middle name. How else is he going to know you're mad at him?
"One Cobra bite and you're falling to pieces!" [Miles, as Frank is complaining about his last overseas assignment.]
Loren Freeman (as Secretary #54): I Got Rhythm
The song that Secretary #54 is singing is "I Got Rhythm" from the George and Ira Gershwin musical from the early 1930s called "Girl Crazy," which featured Ethel Merman. The song would go on to become a trademark tune for Merman.