I love the first Part !  

Well its fiction. Factious is a part of the territory :)

You think the other two are factious, I wonder what you'd think of Second Renaissance (the "future history" of The Matrix). It shows how humanity got from our world, to the eternal twilight of The Matrix. Also taking just the first movie itself, there are several items that are rather farfetched.

Using humans as a power source (humans are consumers of energy and not good producers)
Humans blocking out the sun to fight the machines (but needing the sun for plants/food...)
Where are the items/materials for Zions technology really coming from (too easy...that's what I say)
And what is really the "goop" they eat (I know survival/post-apocalypses depend on some sort of amino-acids or algae, but still...)

Of course most of it is explained throughout the series, but not all of it.