Neither Robert Clampett nor Chuck Jones cared much for this short, not because they thought it was bad, but because it used an iron lung as a gag prop at a time when polio deaths were on the rise.
Daffy breaks the fourth wall when claiming to the audience that he has a sheepskin (university degrees were originally hand lettered onto animal parchment) and a license (in this case, a license plate and not the medical variety).
In the early days of anesthesia operations, the re-breathing bag, which Daffy uses as a punching bag, was a common sight in operating rooms. Modern technology has streamlined the process and the equipment.
A quack is a derogatory term for a doctor, much the same as shyster for an attorney, or lemon for an automobile.