I have been arguing, for instance in my dissertation, that the correctness of Construction Grammar is pretty much uncontroversial. The point, basically, is that no one has ever proposed a semantic theory for even a simple language that doesn't assume the existence of at least one linguistic construction, usually the subject-predicate construction. So in my view those guys over in Berkeley (and their followers) are on pretty solid ground. (The only way I can see to avoid this conclusion is to argue that predication, or function-application, isn't part of the semantics, but something extra.)
Unfortunately, in virtue of not taking explicit account of the role of constructions in their philosophical semantics, philosophers (and linguistic semanticists) philosophers of language have been led to, in my estimation, very implausible linguistic theses. My personal bugbear is the doctrine of logical forms, construed as a linguistic thesis. I want to be clear here that, although I am not convinced of the need for a level LF in syntax, that notion of logical form is far too weak to do the sort of work required by the sorts of robust semantic analyses posited these days. (Think, for instance, of the neoDavidsonian analysis of eventive sentences!) In order to accomodate these robust semantic analyses, the underlying logical forms would have to be vastly more complex than can be reasonably motivated on purely syntactic grounds.
So why have so many philosophers been suckered into accepting them? I'm not sure, but I wonder if it doesn't arise in part from an implicit acceptance of the Fregean view of the language-proposition relation. According to Frege (or, at least, Dummett's Frege), our only cognitive access onto propositions is via the linguistic structure of the sentences that express them. If Frege's Thesis is correct, then the need for a robust semantics will require a correspondingly complex underlying linguistic structure.
[It is also worth considering, in this quasi-historical context, whether or not Russell's notion of contextual definition and the associated doctrine of "incomplete symbols" doesn't mark out an inchoate construction-based theory of language.]