The jaunty little background melody that underscores several scenes in the episode is from Sergei Prokofiev's soundtrack to The Czar Wants to Sleep (1934). The melody has been used many times in film and television shows to indicate busy-ness, or enterprising action.
In the late 60s Dolly would not be the only casualty in modern delivery as the job of milkman itself was about to disappear as well. They were originally necessary because home refrigeration was limited and fresh dairy products came from a central location with industrial-strength cooling and freezing. Eventually better home refrigerators, higher quality milk products, and the supermarket simply made home delivery obsolete. The one holdover though is that many believe milk kept in glass bottles is still far superior to cardboard or plastic.
Walt's dairy company is named Dogwood. Dogwoods are bushy trees common in the eastern United States that sprout distinctive white blossoms in the spring.
There's a baby carriage stored in the Taylor garage, it must be Opie's.
The first scene in front of the Taylor home with Mr. Simpson and Dolly has long shadows in the street from left to right, which suggests accurately that milkmen arrived in the early mornings.