The school house is painted blue. There is a sign that says "The Little Red School House", and "Red" is crossed out. Underneath is another sign saying "Technicolor Red has Gone to War". This is a parody of the wartime ad for Lucky Strike cigarettes which said, "Lucky Strike Green has Gone to War" - as the green on the packages was changed to white.
"Grandma has gone to Lockheed" is a wartime reference to civilian defense workers.
Every time Screwy hits the truant officer dog with one of the "Assorted Swell Things to Hit Dog on Head", the dog's Stetson hat morphs into a hat of another kind. In this order, it becomes a pork pie hat, a sailor-boy cap, a police officer's cap, a top hat, an Indian war bonnet, a witch's conical hat, a bicorne, a crown, a bowler, a fireman's hat, a football helmet, and lastly back to the Stetson.
The big bad wolf remarks that the Screwy Squirrel cartoon must be one of those corny B pictures, a reference to the practice of theaters showing a shorter, less well known (or made) movie (along with a cartoon, a newsreel and some kind of feature short) before the main attraction. These films were known as B pictures (as in A, B).