Time is a wheel to whose kiln is day
& Night a river for we tryst with clay
Lest Kabir sigh or Suhuni frown
Let Sita burn & Rama drown
My Lord, Thou art in every breath I take,
And every bite and sup taste firm of Thee.
With buoyant mercy Thou enfoldest me,
And holdest up my foot each step I make.
Thy touch is all around me when I wake,
Thy sound I hear, and by Thy light I see
The world is fresh with Thy divinity
And all Thy creatures flourish for Thy sake.
For I have looked upon a little child
And seen Forgiveness, and have seen the day
With eastern fire cleanse the foul night away;
So cleansest Thou this House I have defiled.
And if I should be merciful, I know
It is Thy mercy, Lord, in overflow.( There is a Spirit, 1975, p. 13.)
Actually, Nelson's proof was relatively easy to understand, in part because he took the trouble to write out a short outline which make clear the general strategy of proof while omitting most of the technical details (though it was ambiguous at one very crucial juncture), and also because I had already previously thought about the surprise examination (or unexpected hanging) paradox and the Kritchman-Raz argument (see the last section of http://terrytao.wordpress.com/2011/05/19/epistemic-logic-temporal-epistemic-logic-and-the-blue-eyed-islander-puzzle-lower-bound/ ).From the outline one could already see that the main idea was to adapt the Kritchman-Raz argument to the theory Q_0^*, which "almost" proved its own consistency in that it contained a hierarchy of theories Q_1, Q_2, Q_3, ..., each of which could prove the consistency of its predecessor.
Now, I did not at the time fully understand the definition of Q_0^*, nor was I fully aware of the Hilbert-Ackermann result which guaranteed this chain of consistency results, but I was willing to accept the existence of such a hierarchy of theories. (I've since read up a bit on these topics, though.) The question was then, given such an abstract hierarchy, whether one could use the arguments of Chaitin and Kritchman-Raz to establish the inconsistency of at least one of these theories.
These arguments were simple enough (they were basically formalisations of the Berry paradox and surprise examination paradox respectively) that I could then try to do that directly, without any further assistance from the outline. And, indeed, when I attempted to do this, I did at first seem to obtain a contradiction (much as paradoxes such as the Berry or surprise examination paradoxes also lead to absurdity if one reasons somewhat carelessly using informal naive argument). So I could see where Nelson was coming from; but then I spent some time trying to expand out my arguments in detail to find the error. The key, as I found out, was to specify exactly what proof verifier would be used for the Chaitin portion of the argument (this was an issue that was left ambiguous in Nelson's outline), and in particular whether it would accept proofs of unbounded complexity or not. Since Nelson wanted to keep all proofs at bounded complexity, I used a proof verifier that enforced such a bound, and eventually worked out that this could not be done while keeping the length of the Chaitin machine constant; this was the objection that I raised in my first few comments. However, after Nelson responded, it became clear that he was using an unrestricted proof verifier, and this led to a different problem, namely that the proofs produced by Chaitin's argument were of unbounded complexity. So there was not a single "flaw" in the argument, but rather there were two separate flaws, one of which was relevant to one interpretation of the argument, and the other of which was relevant to an alternate interpretation of the argument.
Aside from this one ambiguity, though, the outline was quite clear. Certainly there have been other manuscripts claiming major results that were much more difficult to adjudicate because they were written so badly that there were multiple ambiguities or inaccuracies in the exposition, and any high-level perspective on the argument was obscured.
In my current research project on deduction, I am working on the idea of a dialogical reconceptualization of deduction. One of the upshots would be that the mathematical method itself is able to counter our tendency towards confirmation bias, in virtue of what I call the 'built-in opponent' feature. When formulating a mathematical proof, proponent has to ensure that there are no counterexamples to any of her inferential steps, as if anticipating possible objections by an opponent. In this way, she is 'forced' to adopt the position both of someone who is convinced of the cogency of the claim and of someone who is not.