As I've said many times before, I believe firmly that a film is not about what it's about; it's about how it's about it.
The problem is that what The Damned United is about is absolutely fascinating stuff. The main character, Brian Clough, would be an absolutely ridiculous creation if he weren't based on a real person. His story of an otherwise ambitious soccer ("football" to the film and its native England) manager who gets caught up in outdoing another manager because of a relatively minor slight when they first met is...well, it's wild stuff. And the transformation Brian goes through over the course of six years is stunning, and aptly portrayed by Michael Sheen, in what is surely his more exciting performance to date.
Now if only they'd given it to us straight. This is where the "how it's about it" comes into play, and in a bad way. Sometimes there's a use for telling your story out of order - in this case, cutting back and forth between two otherwise chronological stories, one taking place in 1974 after Brian Clough has taken over as manager for Leeds United, the other taking place between 1968 and 1974 as we see everything it has taken for Clough to get to where he is in the parallel story - but there is absolutely no reason to do it here. All it feels like is a cheap attempt to be clever, one of those notes you get about "keeping the audience interested," as though we're a pack of four-year-olds who need something shiny dangled in front of us every five minutes, rather than a storytelling technique that felt integral to the story.
The extent of your appreciation with thus hinge on the extent to which this bothers you, because everything else in the film is top-notch. Even the overactive camera, mixed with too many cuts and not enough tripods, is often quite striking (especially in director Tom Hooper's use of the camera's focus). As previously noted, the basic narrative, and every performance, is genuinely great, but it's all servicing a tragic misfire of a screenplay.