Howard S. answered 07/11/19
ESL holistic learning with a literary and world-wide perspective
You describe some of the common methods of vagueness one encounters from some speakers, yea even writers.
If you are asking how to scrutinize this, then the best response would be to locate the vagueness and ask precise questions that encourage and even pressure the speaker to recognize the vagueness and remedy it.
For example, you mention this: "Someone may speak with an assumed (but not explicitly defined) context." Given this, you can directly ask the speaker or writer to briefly but precisely explain the context s/he intends.