Development Hell: Not the series, but fan subs were another matter entirely. This series remained practically unknown to the English speaking anime fandom for YEARS. Some years ago, four episodes were subbed but the series was dropped and left in limbo. Luckily, a fansub group named Silver Zero Subs began subbing it in 2010 and continued on for four whole years, and as of today, it's fully subbed.
Ear Worm: The OP will stay in your head for decades.
The series was aired in Spain for first time in 1975. Nearly forty years later it still enjoys the occasional rerun, and it is still one of the few anime shows (together with Mazinger Z, Haha wo tazunete sanzenri -a. k. a. Marco- Science Ninja Team Gatchaman, Dragon Ball, Saint Seiya and Captain Tsubasa) that everybody knows about, even people who are not anime geeks. And "Rottenmeier" has become synonymous with "uptight, straight-laced hag".
Memetic Mutation: One of the most well known memes in the series is an image macro consists of both Heidi pushing a wheelchair with Clara sitting on it, with the next image consists of the photoshopped image of Heidi killing Clara by shoving her down the cliff. The image macros usually goes with joke captions of Heidi's disagreement with Clara's opinions.
Tear Jerker: Heidi's progressive fall into despair as she's away from home.
They Changed It, Now It Sucks: The CGI remake. Aside from the change of animation, the new opening and some minor story changes are considered outright "offensive" by some fans of the original series.