I think that's basically the point - the argument is technically valid, but it is wrong, and you got there by using "human" wrong in the first place.

Well, the problem with the argument 'Socrates is human, humans are immortal, therefore Socrates is immortal' is that the second premise is false. Is it because the word 'human' is used wrongly in the argument? I don't see how. If the problem is that my definition of 'human' is wrong, this still seems to be just a problem of having false beliefs about the world, not an incorrect use of language.