Not historian but professional linguistic anthropologist here so I can answer this question.

First off, the very concept of dialects is flawed in and of itself and associates fully whole languages as subsections of a language with similar origins. Therefore to approach this question the mindset that these Germanic languages were completely independent different language who happened to share a common relatively recent linguistic ancestor must be adopted, they were no more dialects than Parisian French or Castillian Spanish are to Roman Italian.

So onwards to the question, these languages were numerous, with each significant (read not incredibly tiny) state having multiple languages which would be hard to understand between themselves or sometimes too different to understand, at least without extensive effort. In other words, even the same people in a region had languages which could vary so much it was essentially a foreign language. Of course, it should be noted that a great number of words could be nevertheless understood thanks to the fact that these languages were of Germanic, they just simply had evolved in different ways.

Take English for example, if you ever read something in German or French you may recognise an astonishing amount of words, that's because the English language as we know it nowadays is largely an evolution of the language of the Angles and Saxons (Germanic languages) alongside the language of the Norman invaders who spoke a langue d'oïl which would explain the French similarities.

This may have gotten a wee bit too much off-topic so to plainly answer your question, the pre-standarddeutsch Berlin-based language made standard by the Prussians, Germanic languages of nowadays Germany had taken on such different ways off evolving and developing that unless a language was in close proximity to another language and those two had recurring exchanges (which would result in dialects evolving more closely) then the language differences were so great that it was essentially mutually unintelligible although many words could sound similar and held the same origin, just like English is now to German or how Franconian languages sounded foreign to someone from Sachsen.

tl;dr: regional languages had evolved so differently from the original Germanic languages that most languages would be virtually unintelligable, an effect which can be seen in modern day vernacular languages in all societies compared to the state languages (like Picard and Parisian French nowadays).

If you want to learn more on languages and regional differences, in general, I recommend getting Laura Ahearn's Living Language: An Introduction to Linguistic Anthropology which is oft given out of students of general linguistic classes and is amazing.