Red Riding Hood's voice is a comical impression of that of Katharine Hepburn in her title role in "Alice Adams (1935)".
The Turn-Tale Wolf (1952), released over a decade later, was another Looney Tunes cartoon with the motif of the wolf painting himself as the good guy.
Mel Blanc voices Mr. Wolf using a similar cadence to the one he uses for Bugs Bunny.
Grandma is portrayed as a (secret) furrier who specializes in wolf pelt garments. Fur garments were still common wear during the time of this short, especially with wartime rationing arriving. Postwar, fur would evolve into a glamorous accessory piece available to a wide range of women.
The Wolf's compass has directions to Grandma's House, the Three Bears House, the House That Jack Built, and the Three Little Pigs.