I just want to set the record straight for anyone who has never heard of the anthropic principle. This is a principle that says basically that the unverse exists in a way specifically to make life possible. This is often called a fallacy because we make the observation after the fact so it is a little bit of an a priori conclusion, in other words we really do exist so the principle must be true (the conclusion justifies the conclusion but it should be obseration justifies the conclusion).
I think the fallacy of the anthropic principle lies more in its reversal of the true order of causation, and in its illegitimate leap of teleology. Human beings are able to exist because of the very specific conditions of the universe and biosphere, yes, but that in no way implies purpose in general. Nor does it imply that specific kind of purpose which we call design.
I think a clarification of Douglas Adam's parable will help explain what I mean when I say that the anthropic principle has gotten the order of causation wrong. For starters, the analogy is much more abstract than what you seem to think -- the puddle isn't concerned with weak nuclear forces, or rates of evaporation, or humidity, or anything like that. Rather, the puddle is astonished only that it fits into its respective hole so well, and concludes from that observation that the hole was therefore made for the puddle. The part of this soliloquy that elicits a chuckle from the audience is that we, unlike the puddle, are aware that the puddle assumes its shape because of the shape of the hole, not the other way around. Likewise, human beings are what we are (a certain height, a certain metabolism, certain tolerance for heat and cold, etc.) because any variation of organism that didn't occupy this cosmological niche wouldn't survive long enough to reproduce, not the other way around.
The problem with comparing the anthropic principle as it applies to the existence of the universe to the existence of a puddle that feels that its existence is a foregone conclusion is that the universe depends upon a set of constants for its existence (gravitational force, EM force, strong force and other nuclear forces, etc.), whereas the puddle depends upon a set of variables for its existence (relative humidity, the wind, temperature, the presence of shade). Change gravity even a tiny bit and the universe doesn't exist. A little more gravity and the big bang wouldn't have amounted to very much, everything would have collapsed back on itself and there would be no universe as we know it. A little less gravity and the big bang throws particles out faster and farther than they can group into the things our universe is made of. Minute changes of any of the constant forces that govern our universe similarly nullify our existence.
Yes, it would have nullified our particular existence, but I think that using this as an argument for design is still weak. Depending on which cosmologist you ask -- there's obviously a lot of dissension in the field, and I'm not trying to gloss over that -- universes are being created and destroyed all the time, and the only reason our universe has existed in its recognizable form for so long is because it happened to be one in which this fortuitous assemblage of universal constants popped up. To illustrate:
A little more gravity and the big bang wouldn't have amounted to very much, everything would have collapsed back on itself and there would be no universe as we know it.
Such a collapse probably wouldn't go on indefinitely, though -- there are good reasons for the universe to start expanding again. This might have happened billions of times before the universe finally got it 'right'.
Even denying the previous possibility -- which would be understandable given the controversy involved -- there would still be problems in using this "universal" anthropic principle. For why does existence, in the form we narrowly conceive of it, have to be so? Let's say that the second of your hypotheticals occurred:
A little less gravity and the big bang throws particles out faster and farther than they can group into the things our universe is made of.
This precludes natural selection based on chemistry, on assemblages of molecules, but it doesn't preclude natural selection based on, say, differential propagation of electromagnetic radiation. Natural selection is not substrate-specific, so the existence of DNA or even of particles in general is not necessary to its existence. True, this conception of "life" is very foreign to us, but that's the point of criticisms to various anthropic principles.
The universal anthropic principle is precisely the same type of argument as "if Earth's orbit were just a little further from the sun..." and falls prey to a similar criticism, namely that we're conceiving of existence itself (instead of biological life, as in the first argument) anthropocentrically.