Co-directors William Hanna and Joseph Barbera won seven Best Short of the Year Oscars. In order: The Yankee Doodle Mouse (1943), Mouse Trouble (1944), Quiet Please! (1945), The Cat Concerto (1947), The Little Orphan (1948), The Two Mouseketeers (1952), and Johann Mouse (1953).
When Tom said "Don't You Believe It!" it is reference to a radio program from the late-thirties and early forties. The program, hosted by Alan Kent and later Tobe Reed, introduced unique facts along with debunking popular myths, followed by its tagline "Don't you believe it!" The program was sponsored by the Lorillard Tobacco Company, promoting "Sensation" cigarettes.
One of the few times Tom is seen lapping from a saucer of cream. He also resembles an actual cat more in these earlier shorts, with fine plump paws, visible claws, and long whiskers.
The lady mouse ploy says Mae West's catch phrase, "Come up and see me sometime!"
'How to Catch a Mouse' is a 'Random Mouse' book - a play on the publisher 'Random House'.