In its original form, it was fairly specific and made quite strong claims. One claim, for example, was that we humans uniquely have a specialized language organ/section of brain that evolved at some point in time. No evidence has emerged to support this idea as it seems language skills are not concentrated in a single area of the brain (unlike vision for example). And it actually seems implausible that a genetic mutation would produce a language "organ" as it would confer no advantage to an individual in a society where your peers had no language skills.
And you'd imagine that a "fundamental theory" of language would have some practical application but Chomsky's theories don't seem to have any. For example, you'd imagine that it would provide the basis for the study of language acquisition. I remember a friend with a doctorate in clinical child linguistics laughing when I enquired about how their work in therapeutics for children struggling with language problems used Chomsky's theories. Apparently this "fundamental theory" of language has absolutely no application in this area and earlier attempts to apply it led absolutely nowhere. She says that clinicians ignore it - it has no relevance.
Even in AI natural language processing it led nowhere when it was the foundation of AI research in this area from the 60s to the 80s. All breakthroughs in this area use statistical approaches.
I find linguistics fascinating particularly historical linguistics and I used to be quite surprised at how authors in the area seemed to tip-toe around Chomsky's theories - reading between the lines in Guy Deutscher popular book on the evolution of language, for example, he espouses a theory which seems fundamentally at odds with that of Chomsky's (and also seems far more plausible to me than the idea that language ability just sprang into existance through a random genetic mutation) but he seems to go out his way to credit Chomsky's brilliance.
Having observed the villification of Everett - far beyond what I think would have been reasonable - I now understand why linguists genererally either ignore Chomsky's theory or pay some sort of lip-service to give it credit rather than attack it outright. Doing the latter is academic suicide it seems.
As an amatuer in the area, it looks to me like the Emporer has no clothes. It's a theory which is defended vigourously but has no appparent application and is not truly falsifiable. Even when contradictory evidence emerges, the theory is "refined" not into something more useful - the way most scientific theories evolve - but into something vaguer and even less useful.