The title may or may not say it all. I know that there are examples of topological 4-manifolds with nonequivalent PL structures. In some lecture notes, Jacob Lurie mentions that not every PL manifold is smoothable, and that while smoothings exist in dimension 7 they may not be unique, as the existence of exotic $S^7$s shows when combined with the PL Poincar`e conjecture in dimensions other than $4$.
This phrasing suggests that smoothings of PL manifolds are unique in dimensions 1 through 6, which would mean that from the continuum of exotic smooth $\mathbb{R}^4$s we'd get a continuum of exotic PL $\mathbb{R}^4$s. But I haven't yet found a reference for the italicized fact-is it true, or is Lurie's phrasing imprecise, and if it's false, are there even so some exotic PL $\mathbb{R}^4$s?
In this survey article on differential topology, Milnor outlines a proof that every PL manifold of dimension $n \leq 7$ possesses a compatible differential structure, and whenever $n<7$ this structure is unique up to isomorphism. He includes references for the various facts he uses.