This is the very sound distinction that was really standing out to me as an issue in Sacha Baron Cohen's accent in The Trail of the Chicago 7. In that preview, for example, you can hear him say "cops" with a very unrounded vowel - which isn't accurate for the Worchester accent he's going for. That's the major detail that he's missing - otherwise the accent is pretty okay, really, but that's a big issue, and it's the same throughout the movie. (It's not as bad as De Niro's supposed Philly accent in The Irishman, but these are the things that stick in my craw...)
I will say, it wasn't only me. A friend from Worchester went on a rant about it - it's the kind of thing that can really pull a person out of a film.
Note: There were a couple of dialect coaches listed for individuals in the film. There wasn't one listed for Cohen. C'mon, man.