While doing tricks with his egg, Daffy refers to being ready for Edward Bowes, who hosted the famed "Major Bowes Amateur Hour" radio program.
The rolling pins shown in the opening credits are a comic wink at a stereotypical henpecked spouse, being strong-armed by a spouse brandishing a rolling pin.
Divorce, one considered a scandal, had become more common at the time of this short. The adult audiences would have appreciated the very grown up, though subtle, humor of this cartoon.
In addition to being as daffy as his name, Daffy also breaks the fourth wall, which would be one one of his signature moves.