My implicit definition of perfect Bayesian is characterized by these propostions:

1. There is a correct prior probability (as in, before you see any evidence, e.g. occam priors) for every proposition
2. Given a particular set of evidence, there is a correct posterior probability for any proposition

OK, this is interesting: I think our ideas of perfect Bayesians might be quite different. I agree that #1 is part of how a perfect Bayesian thinks, if by 'a correct prior...before you see any evidence' you have the maximum entropy prior in mind.

I'm less sure what 'correct posterior' means in #2. Am I right to interpret it as saying that given a prior and a particular set of evidence for some empirical question, all perfect Bayesians should get the same posterior probability distribution after updating the prior with the evidence?

If we knew exactly what our priors were and how to exactly calculate our posteriors, then your steps 1-6 is exactly how we should operate. There's no model checking because there is no model.

There has to be a model because the model is what we use to calculate likelihoods.

The rationale for model checking should be pretty clear ...

Agree with this whole paragraph. I am in favor of model checking; my beef is with (what I understand to be) Perfect Bayesianism, which doesn't seem to include a step for stepping outside the current model and checking that the model itself - and not just the parameter values - makes sense in light of new data.

I spent a few days wondering how it squared with the Baysian philosophy of induction, and then what I took to be obvious answer came to me (while discussing it with my professor actually): we're modeling our uncertainty.

The catch here (if I'm interpreting Gelman and Shalizi correctly) is that building a sub-model of our uncertainty into our model isn't good enough if that sub-model gets blindsided with unmodeled uncertainty that can't be accounted for just by juggling probability density around in our parameter space.* From page 8 of their preprint:

If nothing else, our own experience suggests that however many different specifications we think of, there are always others which had not occurred to us, but cannot be immediately dismissed a priori, if only because they can be seen as alternative approximations to the ones we made. Yet the Bayesian agent is required to start with a prior distribution whose support covers all alternatives that could be considered.

* This must be one of the most dense/opaque sentences I've posted on Less Wrong. If anyone cares enough about this comment to want me to try and break down what it means with an example, I can give that a shot.