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nshepperd comments on Efficient Charity: Do Unto Others... - Less Wrong
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Functions whose limit is +infinity and -infinity can be distinguished, so your good there.
I think it's the same as my second: As long as the probability given both actions of a humanity lasting forever is nonzero, and the differences of expected utilities far in the future is nonzero, nothing that happens in the first million billion years matters.
The difference in expected utility would have to decrease slow enough (slower than exponential?) to not converge, not just be nonzero. [Which would be why exponential discounting "works"...]
However I would be surprised to see many decisions with that kind of lasting impact. The probability of an action having some effect at time t in the future "decays exponentially" with t (assuming p(Effect_t | Effect_{t-1}, Action) is approximately constant), so the difference in expected utility will in general fall off exponentially and therefore converge anyway. Exceptions would be choices where the utilities of the likely effects increase in magnitude (exponentially?) as t increases.
Anyway I don't see infinities as an inherent problem under this scheme. In particular if we don't live forever, everything we do does indeed matter. If we do live forever, what we do does matter, excepts how it affects us might not if we anticipate causing "permanant" gain by doing something.