I often think of (Alexander) Pope's line in reference to Mary: a little learning is a dang'rous thing (which my father used to quote to me!)

Mary is pedantic, without wisdom or original thought. She is not being (intentionally) funny. She is seriously trying to analyze Mr. Collins's letter as though it were a piece of literature, and in doing so entirely misses the point--the character of the writer. [Perhaps analogous to reading JA and complaining, "but she spells 'chuse' wrong!"]

The reader's amusement lies in the appreciation of Mary's ridiculousness. Many of us may know instances of pedants or academics who overanalyze things, or take things too literally, and miss the entire point of a comment or work! JA may be poking fun at pedantry or a character type, but I am not knowledgeable enough about JA or the era to comment on this.