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How does this work when mining in a pool is nearly continuous? You earn 0.000000x btc per share in a pool, and you might earn a share every few seconds.

What exchange do I use to determine the value of the btc?

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It's likely that the taxable event would occur when you can control the bitcoins. For instance, many pools have a minimum payout and you can't withdraw any until you meet that minimum. Based on other IRS rules, the taxable event would occur when you reach that withdrawal minimum.

As for the exchange to use for the value, it would probably be legitimate to use an average of a few exchanges, if the prices are wildly divergent.

Should emphasize that whatever valuation will be expected to be reasonable and done consistently (so don't pick different exchanges for different payments or whatever, and probably don't pick Mt. Gox, and so on).

Well in the limit it would tend to an integral, and, assuming you have fixed hash power, approach the time and inverse network difficulty weighted average price.

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