This is why casting by origin might be a good thing
The film, overall, is very good. But it was absolutely marred for me by the fact that all the accents were horribly wrong. One must wonder if there was even a single Massachusettian anywhere near the set. I personally don't think so, as the accents that wound up in the final film just wouldn't fly.
Costner's character is supposed to be from Worcester. Costner sounds like a bad exaggeration of a MetroNorth accent. It probably would've been better if he didn't try an accent at all. Worcester people, compared with the stereotypical "Boston" accent (which, might I say, is not actually spoken within Boston proper), do not have much of an accent at all. Just an occasional swallowed vowel.
Greenwood's and Culp's accents, though better than Costner's, were marginal at best. Yes, the Kennedy boys were born in Brookline, but they moved in 1927. By 1962, there's no way their accents would be that thick. And we've got audio evidence to prove it.