"But it bothered the shit out of me that after he'd been blinded he could still 'see.'"
Really? That bothered you? If he can "see" in the matrix (they don't use their physical eyes when they are jacked in and he can see the code at the end of movie one) and can feel the squids (hinting that he is connected to the machine world), what makes it so difficult for you to believe that once he is blinded he can "see" the code? His brain is simply giving him the same sensory feedback that he was receiving in the Matrix.
"There is no indication of a remote hacking ability. And even if it could be explained by some remote hacking ability, it isn't explained by a remote hacking ability. It isn't explained at all."
You could take the Oracle's "the power of the One extends back to the source" as the explanation, albeit a "mystical" metaphor for a technical idea.
I think one of the points of the sequels was to say that things like "love", which we can see as a transcendent spiritual idea, are just words to express things that also have a technical aspect. And that things with technical aspects can be spiritual. It's part of the "Machines are not so different from us" idea. I know the overall idea was that the Matrix represents the "mind", Zion represents the "body", and the Machine World is the "spirit". At the end these have re-connected to make one unified whole.
These ideas are interesting but the brothers tried to ram them all into two sequels and made a giant mess.
This also goes into how he can be in Limbo (MOBILE ave. get it! Yeesh). If he has a wifi connection to the Machine world, his mind can stay in the Matrix without his body being jacked in.
Or he is just a Buddha and he transcended mere logic. Who needs explanations when your enlightened man!
As much as that last statement was a joke, it is possible that we are taking the technological side way too seriously. Perhaps the point (assuming there is one) is transcending the physical. The Architect did seem to be the epitome of logical assholeishness. He didn't get the transcendent nature of human beings but only saw the cold logical program side of us. Maybe the point was that we aren't supposed to know why, but only ask the questions of ourselves. Maybe the Architect IS that side of us that wants all the numbers to fall in line. He will only believe what the math tells him he can believe and will therefore never understand our true nature. The Oracle on the other hand, as the literal Yin to his Yang (see her earrings), is all about exploring our potential which is why she doesn't give any solid answers. That is why the movie ends as it does. Both sides are needed to make the unified whole and a new world is created from that unity by the young girl who is herself a seeming contradiction (a program made out of Love).
I just thought that it may have been more interesting if Neo had fallen in love with a program (or HE was a program!) and the girl was their child. That would have made more narrative sense.
And the name Trinity would have had more significance if they had a child that re-created the world.
PS. They still made two big piles of shit.