Winnie's telling Maynard she wants to watch TV because "I want to see him show up that other doctor: the one that shaves." is a reference to two popular TV medical dramas of the day: "Dr. Kildare" and "Ben Casey." Casey was the doctor who generally had a day or two growth of beard, presumably because he often worked for days without sleep.
First appearance of Duncan Gillis.
The title is based on the common proverb, "A chip off the old block".