Manchester by the Sea is a slow movie. It's a great story with a great script, no doubt. It's shocking, it's depressing and somehow funny at times. To top that, you have a really great organic and natural performance by Casey Affleck who absolutely shines in one of the best characters in movies as Lee Chandler.
There's just a problem. The movie is a drag from scene to scene. The brilliant backstory of the character really holds the movie up, while the rest of it, pulls the movie down. It's not a great experience in the big screen and it refuses to tell the point of the story until 1 hour after it begins. I wasn't a fan of the score either, it makes sense at some points, but at others it's really forced to give it a somber tone.
I think if you have the time, you should definitely check the movie out. Do it at home, though. Also, do it alone and feel it to really take everything away from it. It just doesn't work with friends or the girlfriend at the movies.