Adaptation Displacement: Few children nowadays are introduced to Pippi by reading the books. More often, they watch the movies or cartoons first and might read the books later.
Big Lipped Alligator Moment: From the 1997 animated movie, Blom and Dunder-Karlsson's song of wishing for a bowler and a gold tooth, respectively.
Critical Research Failure: Except from useless pirates that is 300 years late to a country which never even practised pirating (unless you count vikings), do the useless polices in the live action series and movies paradoxically have the police uniforms of 1979, while there appears to only be two polices in the town, despite Sweden since 1973 have been divided into police districts. Also, no governmental organization has had the authority to take a child into custody of the Child-and-Charity-organization, if the child resides in a house that either belongs to a legal guardian or a legal guardian have given to the child. The 1988 movie takes this Up to Eleven.
Strawman Has a Point: In the animated adpatation, Mrs. Pressylus is pretty much the Big Bad who wants to send Pippi Longstocking off to a children's home. She is pretty much portrayed as an Obviously Evil villain... and while some of the things she does is questionable, one actually can't blame her for thinking Pippi should have someone responsible looking out for her. In fact, it's not hard to interpret Mrs. Pressylus as being even more concerned because she thinks Pippi doesn't have a father, judging by how she immediately pulls a 180 the second Pippi's father enters the scene.
Too Dumb to Live: Kling and Klang, from the 1997 film, who obliviously oblige to give Blom and Dunder-Karlsson the tools they need to escape jail. They don't get any better from there...
Values Dissonance: Pippi's father is titled "Negro King of the South Sea" or "Cannibal King". The books were written in the middle of the 20th century, when this was still considered socially acceptable. The Animated Adaptation from 1997 tried to get rid of the Unfortunate Implications by changing it to "Rear Admiral of the Kingdom of Kurrekurredutt", and the modern Norwegian audio adaptations refer to him only as a "King of the South Sea". Astrid Lindgren herself later expressed embarrassment at giving him that title.