In an infinite universe, the speed-of-light limit is not a problem. Surely it limits the speed of computing but any computation can be performed eventually.

wedrifid already replied better than I could; but I'd still like to add that "eventually" is a long time. For example, if the algorithm that you are computing is NP-complete, then you won't be able to grow your hardware quickly enough to make any practical difference. In addition, if our universe is not eternal (which it most likely is not), then it makes no sense to talk about an "infinite series of computations".

For algorithms with exponential complexity, you will have to wait for exponential time, yes. But eternity is enough time for everything. I think the universe is eternal. Even an asymptotically de Sitter region is eternal (but useless since it reaches thermodynamic equilibrium), however the universe contains other asymptotic regions. See http://arxiv.org/abs/1105.3796

Sorry, but I literally have no idea what this means. I don't think that infinity is "like a number but not quite" at all, so the analogy doesn't work for me.

A more formal definition is given in my comment http://lesswrong.com/lw/do9/welcome_to_less_wrong_july_2012/8kt7 . Less formally, infinity is "like a number but not quite" because many predicates into which a number can be meaningfully plugged in, also work for infinity. For example:

infinity > 5 infinity + 7 = infinity infinity + infinity = infinity infinity * 2 = infinity

However not all such expressions make sense:

infinity - infinity = ? infinity * 0 = ?

Formally, adding infinity to the field of real numbers doesn't yield a field (or even a ring).

Well, so far, we have observed one instance of "evolution", and thousands of instances of "no evolution". I'd say the evidence is against the "Law of Evolution" so far...

There is clearly at least one Great Filter somewhere between life creation (probably there is one exactly there) and appearance of civilization with moderately supermodern technology: it follows from Fermi's paradox. However it feels as though there is a small number of such Great Filters with nearly inevitable evolution between them. The real question is what is the expected number of instances of passing these Filters within the volume of a cosmological horizon. If this number is greater than 1 then the universe is more pro-evolution than what is anticipated from the anthropic principle alone. Fermi's paradox puts an upper bound on this number, but I think this bound is much greater than 1