Intermediate-level learners may find the TV shows Sendung mit der Maus and Wissen macht Ah! very instructive. The first one targets young children, and the second one older kids, and they both have a strong educational character, but they are also very entertaining.
Both shows present a series of short features (typically 2-5 minutes long) each answering some question that a young person may have, such as, "how does wind power work?", or "how are balloons made?", or "how come teabags don't fall apart in hot water?", or "why do people say Holzauge sei wachsam!?" (In fact, I think that the ideas for many of these features come directly from questions sent in by the shows' viewers.)
These short films are extremely clear and vivid, which makes them understandable even to those who don't fully understand the accompanying spoken commentary. I'm particularly impressed by the fact that they treat scientific ideas and methods very naturally, as part of everyday life, along with skateboards, ice-cream, rain, and everything else, and without any of the fanfare or otherworldliness that American TV typically slaps onto any scientific content.
The segments are also very imaginative, sometimes whimsical, and sometimes downright hilarious, so they are invariably entertaining, even for viewers well beyond the shows' target ages. (In fact, somewhere I read that the average age of the Sendung mit der Maus viewership is 39! Also, I've been told that it is not unheard of for university professors to "borrow" clips from these shows as audiovisual material for their lectures.)
Lastly, for some episodes there are versions with subtitles in German, although I have not yet found a reliable way to search for such subtitled shows.
Both shows can be viewed online, and one can subscribe to them as podcasts (e.g. through iTunes).