Wittgenstein can help us clarify Locke's problems with language in the Essay, but can Wittgenstein's methods help us to understand the Two Treatises or The Letter on Toleration?
In the First Treatise, Locke is simply giving Robert Filmer a much-needed Bible lesson. In the Second Treatise, Locke presents a picture of human nature and human history, offering suggestions on how we might build institutions to protect that world view and the people in it. It's all politics. With a nod to political science, in the classroom we must unpack the Second Treatise wearing the hats of anthropologists and historians.
Methodologically--perhaps--Wittgenstein shows that Locke's remarks and recommendations in the Second Treatise are not matters for philosophers to argue over but are rather the stuff of political debate: matters that are introduced in grammar schools and settled in Parliaments--and upon battlefields.
Not sure if this reflects Wittgenstein's methodology, but he might agree with Locke. And would he say that when it comes to cosmological foundations, Hobbes's materialism is unproven scientifically (indeed, laughable--and so toxic as to merit contempt and ridicule?), while Locke's skepticism in discussing the "science" of cosmology and physics is the appropriate response to the subject--and still is, I should add.
Which leads to a related question regarding contempt and laughing at Hobbes. What are we to say to our colleagues who, with much fanfare and middle-brow sanctimony, actually think that Hobbes' cosmology/physics and anthropology is "scientific" or "the settled science"?
Talking a step back from the whole thing: where Wittgenstein most agrees with Locke--perhaps--is in using language diplomatically to bring people together and "gently" suggest rather than to argue forcefully or stridently. As Peter Laslett (if I recall correctly) suggests, if The Letter on Toleration represents the foundations of Locke's approach, then the most important thing philosophers can do is bring people together--and agree that there is some "truth" out there, and that we should work to find it, though, alas, we might never arrive at it. Nor should we expect to... Meanwhile, what can we do to improve each other's lives?
Hobbes--and his ilk, and there are a lot of them--ape the patterns of civil discourse, but rather than advancing the interests of people in society, they rather advance the interests of cohorts, elites, viral mass-formation cult behaviors and the special interests of parties who use human society as a means to their own ends.
In answer to the question that opens this note, it seems that Wittgenstein offers very little, except the model of a very rich and eccentric man who is sometimes outspoken, but who otherwise is addressing a cohort of university intellectuals rather than society. And by society (I should have said this earlier) I mean of course Locke's definition of human society, which forms because it is a characteristic of human nature, and which therefore proceeds the state.