The title is from the nursery rhyme "Mary, Mary, Quite Contrary". The rhyme has been seen as having religious and historical significance, but its origins and meaning are disputed. It has a Roud Folk Song Index number of 19626.
One of the few times the role of the antagonists is reversed. Tom genuinely wants to be left alone so he can sleep, but sleepwalking Jerry won't have any of it.
The large S shaped iron piece on the side of the chimney was used to support the brick work in older homes. Another common motif was an X.
Chuck Jones had been working on the TV animated special, How the Grinch Stole Christmas, released the same year. Tom looks decidedly like the Grinch in side profile here, something that had become more apparent as Jones developed the other work's storyboards.
The music has an upbeat 60's sound, with a little bit of espionage-style bass line to counter.