The paranormal was a subject of interest at the time, both in films and real life. Wartime research included the use of hypnosis in many situations.
A WW2 reference is shown at the end of this short, to the B19 bomber. Such patriotic messages were common in wartime, even in cartoons and magazine ads.
Elmer breaks the fourth wall several times in this short.
The earlier Bugs appears here, with his more pronounced, wisecracking demeanor, New York City-esque accent, and pinker ears. But he still manages to kiss his enemy, something he'd do throughout his career---along with breaking the fourth wall.
In the beginning, Elmer Fudd is walking with his rifle strapped to his back pointing up. Common knowledge among gun owners is that one's gun should always point away from anything that could be hit when not in use. In this case, it should be pointed down. Then again, the show has always played with guns in the early years to cartoony, non-lethal effect.