The movie theater has a painting of an unclothed female above the curtains at the top of the stage.
Bugs gets a carrot from a vending machine with two pennies taped to it. This is a reference to cigarette vending machines of that era, which often dispensed cigarette packs with the correct change taped to them.
Elmer's 'Wabbit Detector' resembles Mine Detectors of the World War II era, which were based on metal detectors of that time.
Military surplus was a huge enterprise in the immediate postwar era. Surplus items appear in several WB cartoons as well as feature films.
A 'masher' is an archaic term for a male troublemaker, used both pre- and post-WW2. More than just a troublemaker, a masher was a guy making unwanted sexual advances.