These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Germans Love David Hasselhoff: Heidi is a classic in the German-language sphere as well as the world, but it is notably popular in Japan and Turkey.
But apparently not Purity Sue enough for Fraulein Rottenmeier. It's hinted that Rottenmeier has been reading books featuring Swiss girls that were even bigger Sues than Heidi ("I thought I would look for a little Swiss girl, as I hoped to find such a one as I have often read about, who, born as it were of the mountain air, lives and moves without touching the earth") and is disappointed that Heidi doesn't live up to this impossible standard.
Fair for Its Day: Heidi and Klara are characters from a novel written in 1880, for readers of that time frame. So they're Purity Sues by today's standards, but not for the time they were written.
Nightmare Fuel: So, so much in many of the adaptations. Fraulein Rottenmeier is one of the egregious examples of this in a few of the cartoon versions, but especially in the Hanna Babera film "Heidi's Song." There's one part where she turns into a fanged witch and...well, you should really just watch it for yourself. Or don't, if you'd like to sleep again.
Tear Jerker: Come on, try not to go for the hankie when Klara finally leaves her wheelchair.
Or Heidi's Heroic BSOD that leads her to become a sleepwalker because she cannot stand being away from home.
To a lesser extent but still applies, when is hinted at Alm-uncle backstory that he left the army not for a murder, as often rumoured, but for the death by illness of an officer he had under his care as a male nurse sort of way, and said death was the beginnig of his breakdown. Consider now that the first time the reader have access to those memories is by association with Clara, and that by helping her recover he appears to be paying tribute to a man he admired and could not help, and...
Values Dissonance: It's strongly implied that Heidi's sleepwalking spells are caused by a propensity to epilepsy - her Missing Mom Adelheid had seizures ("curious attacks, during which no one knew whether she was awake or sleeping"), and at the time the book was written epilepsy was thought to be inherited.