Assuming you are referring to what is often called the "teleological proof", the proof is indeed sound (and, isolated from the noise of the angry agnostics/atheists, is even obvious). The argument is based on statistical induction, the same cognitive methodology that is behind all of the natural and social sciences, as well as basic, rational thought. The construct of the argument is fairly simple and, like all proofs about the real world, involves taking something we already know, and interpolating from it to something we originally did not. In the case of teleological reasoning, it is actually the exact same proof we use when we assume that other people exist (albeit somewhat stronger since in those applications there is technically more room for attacks based on the possibility of intentional deception, which would not apply here since the whole point is to show intention to begin with).
With regard to your specific questions regarding the obvious differences between artificial machines and natural ones, the argument does not induce all properties from the known relationship to the unknown. Using Occams' Razor, one only induces the minimum "properties" necessary to explain the phenomenon.
The argument is essentially the strongest form of what is known as hypothesis testing. When a scientist proposes a model to explain observed phenomena, he tests the models ability to explain the phenomena relative to the null hypothesis, namely, the likelihood that the phenomenon would be observed at random even if the model model/hypothesis were false. The criterion generally accepted to "prove" a hypothesis is 95% or in stronger studies sometimes %99. In the case of the teleological proof, the criterion reached is 99.99999999999... which is as close to certainty a proof in the natural sciences could ever get (and, indeed, in no other instance do other such proofs come close.)
Getting to the actual proof, the observed phenomena upon which the inferrer bases his inference are:
- his own existence (which includes his observations of his own intentions/conscious choices as well as of his own ability to control and design his environment to reflect his intentions);
- the changing medium/environment in which his intentions are expressed, including both changes that he observes to correspond to his own expressed intentions, as well additional changes that he does not observe himself to be in control of.
- the partial similarity between those changes he observes as self-initiated and those that are not observed as self-initiated.
Based on this information, he is able to infer the presence of another mind behind those environmental changes. Based on how similar the other-initiated changes are to the self-initiated changes, the inferrer can infer the level of similarity between the intention of the detected other and his own intentions. This process is known as Theory-of-mind. As you note, in the case of natural phenomena, there are large differences from artificial ones. This is why teleologists do not assume man made the natural universe and rather that the Mind behind it is quite different. But the same basic logical argument is used in infering both man and G-d.