Somehow it doesn’t seem surprising that Daniel Ellsberg, the former U.S. military analyst who leaked crucial Vietnam War documents to the press in 1971, is also a magician by hobby. After all, the reveal of the Pentagon Papers was like a great disappearing act in reverse. Here were materials that no one knew existed, direct from the highest order of government, confessing that the officials in charge of the ugliest war in American history had deliberately misled the public about our progress in the region for over a decade. And here was Ellsberg, apparently the only man in Washington with a conscience, risking life in prison to tell people the truth.

In the Oscar-nominated documentary “The Most Dangerous Man in America: Daniel Ellsberg and the Pentagon Papers,” we see the now-79-year-old Ellsberg briefly perform a magic trick called the Square Circle. The former Detroiter remains spry and alert nearly four decades after his name was plastered across every media outlet in America. He’s embraced his role as a firebrand who believes in truth and utter transparency at all costs (sad, in a way, that America needed Ellsberg to remind us of these values). When Ellsberg recounts his story, it’s not with a self-righteous air of entitlement, but rather a matter-of-fact demeanor that plainly states that going against the Pentagon was the only thing he could do.

So the real-life story surrounding the Pentagon Papers is gripping, and Ellsberg in the flesh is a fascinating man. But unfortunately, the film’s presentation can’t quite live up to the intrigue of its subject. Judith Ehrlich and Rick Goldsmith, the co-writers, directors and producers, have a very small amount of combined filmmaking experience between them, and the production values of “Most Dangerous Man” are more PBS than Oscar.

The attempts by Ehrlich and Goldsmith to give their film stylish touches are clumsy at best, distracting at worst. It’s common for historical documentaries like this one to employ re-enactments when no archival footage is available, but the staged sequences here are ridiculously uninspired, to the point where one must question why they were even necessary to the narrative. An Ellsberg lookalike takes notes and makes phone calls, then studies flashes of dramatically lit pages as low-rate “suspense” music plays incessantly in the background; it’s like a retro episode of “Law & Order.”

Besides those moments and some weird, out-of-nowhere animated interludes, though, “Most Dangerous Man” does a competent if unremarkable job of telling Ellsberg’s story. The narrative picks up in the second half of the film, after the unveiling of the papers, when the man becomes emboldened by his singular drive to get them seen. He sends them first to The New York Times then to every other newspaper in the country. He even gets former Alaska senator Mike Gravel to read the papers out loud on the Senate floor so they’ll be entered in the public records.

Thanks to the account of these stealth missions and scene-stealing audio recordings of then-president Richard Nixon’s private rants (in which, among other things, he refers to Vietnam as a “shit-ass little country”), the film goes out on a much higher note than its occasionally plodding first half. Above all, the movie still informs, which should be the primary goal of any documentary. Yet, somewhere between the stock footage of Vietnam atrocities and the brief tidbit that all of Ellsberg’s former employees and friends treated him like a traitor, “Most Dangerous Man” proves unable to penetrate the real emotional truth of the story. The man is there, but the danger is not.