Red Riding Hood's voice is a comical impression of that of Katharine Hepburn in her title role in "Désirs secrets (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.
"Jiggers!" is an outdated slang interjection for "watch out!"
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.