The nephews make a reference to Seabiscuit, a very popular Thoroughbred racehorse at the time this short was released.
The horse is designated '4F' which is the military code for 'Disabled and Unfit for Military Service', which would be well-known to most people at the time of this short's release - the middle of World War II.
Popeye wears his all blue sailor suit, but has an orange and white striped undershirt on beneath. This might have been added to give more color to the cartoon for the audience to notice.
The mailbox reads "J. Tyer," a nod to animator James Tyer.
As the nephews pretend to sleep, their snores play the opening of Ludwig van Beethoven's 5th symphony. The four tones spell the letter "V" in Morse code, a reference to the WWII slogan "V for Victory".