Has the "dismal theorem" practical implications?
My conclusion based on reading his paper is that the utility function of an individual or society can't be of the CRRA form presented in the paper. That would indeed lead to scenarios where you could not get out of the bed in the morning, as minimizing the tiniest probability of an enormous risk would warrant infinite sum of money.

I will attempt to explain the mathematics of the paper. First the utility as a function of consumption is of the form:

$$ U(c) = -c^{1-a}, \space a&gt;1$$

This is also called a constant relative risk aversion utility function. Constant relative risk aversion with regards to consumption means that a person prefers a bundle of 1 utils over uncertain bundles with expected value of 1 utils. The same applies to 2 utils to the same degree proportionally. Note that the utility is $-\infty$ when consumption reaches 0. 

Now, if you want to calculate the exact utility that a person receives you simply multiply the probability of each bundle with the utility it grants:

$$P_1*U(C_1)+P_2*U(C_2)... = \sum_{n=1}^{\ b}P_n U(C_n)$$

Where P denotes a probability of a given bundle and U(c) is the utility.

Finally, consider a case where there is a possibility of a bundle that has consumption value of 0, with probability greater than zero:

$$ P_x U(c_x) = -\infty $$

It does not matter what the probabilities and utilities of other bundles are as you can't recover from minus infinite utility.

The same principle applies to continuous probability distributions, so just replace the sum sign with an integral and consider case where it doesn't reach 0 probability when c=0.

You may be interested in readin Nordhaus's response:
http://aida.wss.yale.edu/~nordhaus/homepage/documents/weitz_011609.pdf (By the way, he uses the exact same case scenario as I did).