Simply put, Black Mass is the story of an Irish mobster and generally really bad guy (Bulger) hopping in bed with the FBI in an effort to bring down the Italian mob in South Boston. His motives are pretty crappy, as are his morals and his ability to serve as a useful informant. Agent John Connolly maintains that Bulger is a vital connection, but sometimes it seems like he just enjoys being tied to a family with so much more power than his own. (Whitey's brother Jimmy, played by Benedict Cumberbatch, is a successful state senator.)
Though we are given occasional glimpses of Bulger's softer side when he returns home to his child bride (Dakota Johnson) and young son, there's something off key about how it's presented. You're agog that a Whitey Bulger would be with a Dakota Johnson, so you're mentally trying to figure out if he's her dad and maybe she's a single mom? And is he even old, or is he just very white and balding? What is happening? By the time Bulger's son is hospitalized with Reye's Syndrome, this pivotal event is diminished by the fact the family scenes all played like he'd walked into the wrong house.
The same is true of the movie as a whole. There are a lot of meetings and periodic crimes, but nothing holds much weight. We see John Connolly slowly being absorbed into Bulger's world at the expense of his marriage and his soul, but it's something we witness from afar, not something we feel. Bulger's ultimate downfall and the crumbling of his empire is similarly lackluster. It all unfolds in front of you, but it's never clear why we should care.
Bonus features on the Blu-Ray + DVD + Digital HD edition include the featurettes "The Manhunt for Whitey Bulger", "Johnny Depp: Becoming Whitey Bulger", and "Black Mass: Deepest Cover, Darkest Crime". The standard DVD includes the featurette "Johnny Depp: Becoming Whitey Bulger".