The argument that the universe is "fine-tuned" to produce human intelligence is interesting on so many levels, from the limits of our physical theory to the problems of estimating probabilities from a sample of one (universe). To me, however, the most interesting part of the argument is the way it recapitulates the ancient human urge to project ourselves onto the universe as its purpose. Many quite scientifically-minded folks have been swayed by arguments that the universe was built to produce us.
A basic tenet of the strong fine-tuning argument is that only a universe
set up the way it is could produce intelligent life. The physical
constants have to be just so, or we couldn't exist, and therefore
intelligent life couldn't exist. See the sleight-of-hand there?
I'll come right out and say it: I think this is basically solipsism in disguise, but that's not much more than name-calling. Let me do better and give you an analogy.
Consider Picasso's masterpiece Guernica. Imagine it was the only piece of art known to the world (it's an analogy, OK?). We could tell a long narrative about the historical events that inspired Picasso to paint it. We could point out how a bullfighting motif is central to the symbolism of the work. We could even discuss the oil pigments, brushes, and canvas that had eventually made their way into Picasso's hands. Our story would be full of specific historical events (the bombing of a villiage during the Spanish Civil War), contingencies (the Germans lending air support to Franco), and happy accidents (pigments discovered that reflect light in the narrow visual range of the human eye, oil paint reaching the naval power of Venice in the 15th century, where sail canvas was easy to get). It could be a very long and detailed causal network that resulted in this particular painting.
We could probably all agree that without all those events, contingencies, and happy accidents, Guernica would not exist; too many specifics of the painting have been triggered by those antecedent events. This is the metaphor's equivalent to human intelligence; there are so many crucial events in the causal chain to Homo sapiens, from the cooling of the early universe to form electrons, protons, and neutrons, to the formation of heavier elements in second-generation stars, to evolution of a DNA-based genetic system in early living things, to locomotor animals which benefit from central nervous systems, to the vocalizations and social systems of our recent ancestors which drove the development of symbolic language and culture. Without all those events, and the physical conditions that made them possible, our particular form of life would not exist.
The advocate of fine-tuning, however, goes one huge step farther. He or she does not just see our specific form of life as contingent on the current conditions of the universe; all possible forms of intelligent life are contingent on this universe. There could have been no life without the universe being carefully set up the way it was, because life (like the form we know) would be impossible if things were different. Lower the strength of the strong nuclear force much, and there's no iodine, and we all know iodine is essential to life...
To return to the Picasso metaphor, we can all agree that without Franco, oil paint, or the Wright flyer, there could be no Guernica. The fine-tuning argument is like a claim that without Franco, oil paint, or the Wright flyer, there could be no art.