I've always thought this argument of Putnam's was dead wrong. It is about the most blatant and explicit instance of the Mind Projection Fallacy I know.
The real problem for Putnam is not his theory of chemistry; it is his theory of language. Like so many before and after him, Putnam thinks of meaning as being a kind of correspondence between words and either things or concepts; and in this paper he tries to show that the correspondence is to things rather than concepts. The error is in the assumption that words (and languages) have a sufficiently abstract existence to participate in such correspondences in the first place. (We can of course draw any correspondence we like, but it need not represent any objective fact about the territory.)
This is insufficiently reductionist. Language is nothing more than the human superpower of vibratory telepathy. If you say the word "chair", this physical action of yours causes a certain pattern of neurons to be stimulated in my brain, which bears a similarity relationship to a pattern of neurons in your brain. For philosophical purposes, there is no fact of the matter about whether the pattern of neurons being stimulated in my brain is "correct" or not; there are only greater and lesser degrees of similarity between the stimulation patterns occurring in my brain when I hear the word and those occurring in yours when you say it.
The point that Putnam was trying to make, I think, was this: our mental concepts are causally related to things in the real world. (He may also, ironically, have been trying to warn against the Mind Projection Fallacy.) Unfortunately, like so many 20th-century analytic philosophers, he confused matters by introducing language into the picture; evidently due to a mistaken Whorfian belief that language is so fundamental to human thought that any discussion of human concepts must be a discussion about language.
(Incidentally, one of the things that most impressed me about Eliezer's Sequences was that he seemed to have something close to the correct theory of language, which is exceedingly rare.)
The real danger of thought experiments, including this one of Putnam's, is that fundamental assumptions may be wrong.
That's an interesting solution to the problem of translation (how do I know if I've got the meanings of the words right?) you've got there: just measure what's going on in the respective participants' brains! ;)
There are two reasons why you might not want to work at this level. Firstly, thinking about translation again, if I were translating the language of an alien species, their brain-equivalent would probably be sufficiently different that looking for neurological similarities would be hopeless. Secondly, it's just easier to work at a higher level of ab...
Thagard (2012) contains a nicely compact passage on thought experiments: