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Not well versed on the specific jargon in English grammar, I seek clarity on the usage of the expression "following a/the discussion, ...", as I vaguely remember some "rules" about not mixing different subjects in a sentence.

The following examples seem to use the expression "following a/the discussion" in different manners,

Example 1

Following a discussion of disability policy, we explore global concerns and initiatives

The sentence is constructed using an active voice and there is only one subject we -

We first had a discussion of disability policy. Then we explored global concerns and initiatives.

Example 2

Following a discussion of this four-system framework, the fascinating clinical phenomenon of unilateral neglect or hemi-inattention is discussed

The sentence is constructed using a passive voice. As a result, there are two subjects. Subject 1 is a four-system framework and subject 2 is a phenomenon. Both subjects were discussed in the chapter/paragraph/book.

Example 3

Following a discussion of the merits of the various notations, the reader is introduced to the ubiquitous Gauss' divergence theorem.

It appears that this sentence is constructed in a mixed active-passive-voice manner and as a result, there are two different subjects embedded in this single sentence. First, a paragraph/chapter discussed the merits of notations (active voice). In the next sentence, the reader is the subject but is expressed in a passive voice.

Are all 3 examples considered grammatically correct or would the 3rd example be considered unnatural and incorrect because the sentence mixes two verb voices and use two different subjects, as opposed to (a) a single subject with an active voice or (b) two subjects with passive voices, which can be converted into an active voice sentence by using another single subject that exerts an active voice on the two subjects as objects?

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The phrase "following a discussion..." is a preposition phrase used as an adverb of time or manner modifying the following main clause. While you can infer who was doing the discussing, it's not strictly implied, and has nothing to do with what the subject is in the main clause.
In your third example, presumably the discussion was in the text of the book, and the reader was introduced to the theorem after reading the discussion. "The reader is introduced..." is still just a passive voice expression.

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