How to compute the disagreement between hypotheses
One major task of computational learning theory is to try to handle questions like this for specific classes.  In general, if you assume no structure on the hypothesis space, you basically have no choice but to look at each hypotheses individually.  On the other hand, if there is a lot of structure, eg. if you assume the hypotheses are linear separators, say in $\mathcal{R}^2$, you can see that it's possible to be quite efficient even though there are infinitely many linear separators!

The same thing happens for trying to find the ERM (empirical risk minimizing) hypothesis in a class.  This is important for PAC learning. Sometimes it's easy, sometimes it's not.