The "Katy did, Katy didn't" gag was later incorporated into a song for the Fleischer Studios movie, "Mr. Bug Goes to Town."
Showing Betty attired in stylishly fashionable pyjamas, modest though they were, was pushing the envelope of the newly enacted Hays Code at the time.
The first mosquito causes Betty to experience the bane of women at the time, a run in her stockings. They were likely made of silk, as the new nylon version would not be introduced until the 1939 World's Fair.