The biggest problem with these computations that take all the mutations that ever happened and then whomp up some kind of factorial result by stringing together all the generations is simply that ... each generation is mathematically on its own!
If I am reading you correctly, you're talking about Climbing Mount Improbable, to use Dawkins' colorful (or would it be colourful??) expression.
I've referred to it in the past as the "second-floor frog fallacy" The creationists' argument is the equivalent of saying that frogs could never get to the second floor of a building, as it is twelve feet above the first floor. They say, "no frog can jump twelve feet into the air, so there can be no frogs on the second floor." This ignores, of course, the staircase...
That's a good one, and it's in the same general area of fallacies, but not quite the same as "incorporating the continuum." Here's another example of -- ahem! -- my fallacy: you cut the cards, and then start dealing them out, one at a time. The resulting array has the awesome probability of one in 52 factorial, which is, more or less, one in 8.06581752 × 1067. However, as to any one card's chances, the odds are nowhere near as great.