Hmm...I would have guessed that everyone could understand Hochdeutsch,as it has 'official' status.Wouldn't it be the language that is broadcast on newscasts and regular TV shows,or is a lot of that also done in local dialects?
You have to differentiate between the active and passive vocabulary or word pool. Like I can read or understand practically every text in English, even scientific and higher literature, but my active vocabulary is way smaller than that. Similarly, there is a difference between understanding someone talking or talking fluently, as you might guess.
Older, less intelligent and less educated people have still, in many areas, troubles with speaking truly fluently and on a high level in the high level language. Funnily, the situation has largely reverted from where the High German Standardsprache came from, simply because Plattdeutsch is largely dead. The original Plattdeutsch was more similar to Dutch, which, like the name suggests (Dutch = Deutsch) is just a German dialect which branched off to an own language, largely because they made it their written language. Contrary, the Plattdeutsch zone had to reinvent itself and is now largely defined by a harder pronunciation and some additional vocabularly, whereas the basic vocabularly and grammatic is, for most regions at least, much closer to Standard German.
In areas in which High German dialects were spoken, this kind of reinvention and adaptation to the Standardsprache never happened, because these dialects were always fairly close to it. So you have now the funny situation that in the areas from which the Standardsprache of German came, you have quite often more, stronger and more widespread dialects, than in the zones which spoke a completely different dialect before, like in the Plattdeutsch North.
The Allemannic South West with Swiss German is another extreme, because it developed such a strong regional dialect, that if making it a written language too, it would have been not as different but fairly close to Dutch-Flemish in its distance from Standard German. But that never happened. Here too, the well educated people often speak a very clear cut high German, if they want, because its almost a second language for them. For someone from Bavaria, much of Austria, Thuringia or the Rheinland, the difference is still big, but by far not as big between the dialectal Umgangssprache and the Standardsprache. But of course, in the past, in some remote villages, people oftentimes spoke some unintelligible jabbering at times, especially if it was a really small and isolated village, because the smaller the number of the illiterate speakers, the quicker and easier a language gets stunted.
Its amazing how quickly many terms can get lost. I mean not just changed, but simply got lost. People have no expression for the matter any more.