I've read a number of criticisms of Paley's watchmaker argument, but I've never seen one from the standpoint of an anthropologist. It would be fitting: after all, when we find artifacts, anthropologists are the ones trained to interpret what they tell us about their makers.
Presume a far-future anthropologist who discovers the watch. It (and I choose it because it may not even be of our species) is initially unfamiliar with watches.
Yes, the anthropologist would likely conclude that the watch was designed. It might even conclude that the watch, circa 1800 and obviously crafted by hand, was made by one "designer" or artisan.
But the anthropologist would not stop there. There is much more information inherent in the watch. Everything about the watch shrieks that there is more than just a designer. The diverse materials of the watch speak of commerce, of industry, of technology. No one designer would have assembled all those raw materials, purified and processed them into glass and metals and alloys. Nor would one designer be genious enough to invent all the technologies embodied in the watch (springs, gears, hands, numbers on the watch face, tools for manufacture, etc.); those obviously imply a long period of technological development. Nor would one designer devote such vast labor to invent and perfect the design to such an extent just for himself: the design speaks of use by customers. Indeed, the anthropologist would be very surprised if this was the only watch ever made, and would search for more.
The anthropologist would find numerous other timekeeping devices (as well as whole loads of other devices.) It would perceive patterns of historical development and spread of the technologies that compose watches and the other artifacts, and find evidence of myriad watchmakers over a long period of time, who produced timekeeping devices ranging from sundials to atomic clocks. The evolution of timekeeping would be seen to occur in gradual steps, except where other technologies that had themselves evolved gradually, were integrated for timekeeping.
Our hypothetical anthropologist looking at the watch would not conclude only that there was a watchmaker: we would conclude that the watchmaker was a member of an enormous technological civilization.
Wait: say the anthropologist found a plant of Zea mays, corn. Everything about the plant screams that it is unnatural and created: it requires dense stands for pollination to work, there is no natural dispersal mechanism for the seed, it cannot compete with ordinary plants, it's lacking most of the important chemical and mechanical protections for its seeds that wild plants have, etc. The anthropologist would obviously conclude that corn is artificial. But it is not consciously designed. A continuum of ancestors leading all the way back to a wild grass, teosinte can be found. The anthropologist could conclude that corn had a designer, but he'd be wrong. Corn didn't come about by a process of design: rather a process of selection among natural variation over a period of a hundred or more human generations.
What have we learned from this thought experiment? Besides the basic fact that the watchmaker argument is a very weak argument by analogy?
First, that slight extensions of the analogy lead very quickly to conclusions that Christians would not enjoy, such as the idea that their god is a mere watchmaker in a much more extensive culture of gods.
Second, that a slight change of the analogy to another human artifact that was created by humans but NOT designed can lead to an invalid conclusion of design. In other words, we are incapable of accurately discerning design from selection. Unfortunately, William Paley did not provide an analogy for discerning theistic selection from natural selection.
(What is this doing in this blog? I had no other really convenient place to put it right now. If anybody would like to provide a more appropriate home, let me know.)