Blom and Dunder-Karlsson in the 1997 animated movie. Considering how they mean no real harm towards Pippi, and how their motivations are revealed to be relatively harmless in their "I Want" Song, they could be analyzed as a couple of tragically poor buffoons who desperately want to live a better life. On the other hand, they make no qualms about robbing a little girl blind, and they had to have done something to land themselves in jail in the first place.
Mrs. Prysselius in the animated adaptation as well. In the 1969 TV series, she was certainly a bit overbearing, but she was genuinely concerned for Pippi's well-being, considering how Pippi was possibly an orphan who needed proper adult supervision to avoid running into dangerous situations, or even causing any trouble, as she was admittedly a rather loose cannon. However, in the 1997 film, it seems she has no concern for Pippi's safety, only wanting Pippi in the children's home so she could maintain her vision of order in the town by having Pippi out of the picture, and the fact that she sends two (albeit harmless) criminals to capture her supports this, making her a persistent Control Freak.
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. While it does have a catchy tune and offers an introduction to these two and their motives, it comes right out of left field and is never addressed again afterward.
Critical Research Failure: Except for useless pirates that are 300 years out of date to a country which never even practiced pirating (unless you count vikings), the useless police in the live action series and movies paradoxically have the police uniforms of 1979, while there appear to be only two policemen 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 has given to the child.note According to the first book, Ephraim bought the house years ago, as a place to live when he retired. He could have made her co-owner legally, or simply put the house in her name, anticipating he'd be away a lot. The 1988 movie takes this Up to Eleven.
The songs in the 1997 animated movie can qualify as well. For instance, anyone who grew up with the film can just type "Standing on top of Mount Kilimanjaro..." and they'll be mentally singing the opening number.
Also from the 1997 animated movie: "I want a bowler, an English bowler..."
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. Lindgren made it clear early on that the Kurrekurredutt were not really cannibals, having given it up many years before Ephraim was there. 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.