For a little further background, what I'm really asking here is how linked in to the "science news" of the day could I be? Would it just be some heavenly sign with no context, or would I be more like "ah yes the priest said the bishop said he got a letter from Rome saying we are seeing something last seen 75 years ago"? Or would my understanding be completely linked to education or class regardless of location?
I'm mostly curious how much of an elite or localized phenomenon more cutting edge ideas were in Europe at the time. It's a bit anachronistic to call it science or even "natural philosophy"...but that's more or less what I'm getting at.
/u/mikedash has an amazing, multi-part answer on the range of meanings attached to Halley's comet and other astronomical signs and wonders in the Middle Ages!