Presumably the special effects budget for “Snowden” wasn’t sufficient to allow Oliver Stone to place a halo over the head of Joseph Gordon-Levitt, playing the whistleblower who in 2013 released proof of the US government’s widespread scrutiny of ordinary Americans’ phone records and computer logs, as well as intense surveillance of foreigners, including important officials. Perhaps to make amends for the omission, Stone concludes the picture with some scenes of the real Edward Snowden in the Russian apartment where he now lives as an exile, showing him bathed in sunlight that can only be termed heavenly, even if the expatriate himself is not a religious man.

That isn’t to say that what Snowden did wasn’t extraordinarily important, or that he didn’t exhibit a remarkable degree of courage in putting himself on the line in doing it. But Stone’s treatment has more than a whiff of hagiography to it. It also lacks the sheer cinematic verve that’s marked much of his previous work—sometimes to excess, to be sure, but at least bringing a sense of energy and propulsion to the stories he was telling. In this case he’s working in a more solemn, earnest mode that frankly comes across as tame and pedestrian. At the one extreme there are “JFK” and “Nixon,” frantically impassioned polemics that can careen off course but can’t help but engage; at the other are “World Trade Center” and now this film, which attempt to honor their subjects but end up feeling didactic in a fashion that’s more drab than dramatic.

Stone and his screenwriting collaborator Kieran Fitzgerald employ as a framing device the time that Snowden (Gordon-Levitt) spent in hiding at a Hong Kong hotel with documentarian Laura Poitras (Melissa Leo), reporter Glenn Greenwald (Zachary Quinto) and veteran journalist Ewan MacAskill (Tom Wilkinson), the latter representing the Guardian, the paper that would be instrumental in vetting and printing the reams of material he had taken from the Hawaiian CIA counterintelligence facility where he’d worked as a contract analyst. These events make up the substance of Poitras’ fine documentary “Citizenfour,” and while the recreation is well done, it nonetheless pales by comparison to the real thing.

While the days in Hong Kong proceed, the film slips periodically into flashback mode to dramatize how Snowden got there. These scenes begin with a sequence showing him, frail and undersized but a dedicated patriot in the wake of 9/11, failing to qualify for Ranger service in the US Army, actually suffering a severe injury during basic training. He then applies for the CIA and is accepted into training by his interviewer Corbin O’Brian (Rhys Ifans), who appreciates the recruit’s computer skills despite a lack of even a high school diploma. Once settled in for tests, Snowden shows himself an exceptionally able computer specialist, impressing O’Brian so much that he becomes the young man’s mentor. Snowden also wins the admiration of Hank Forrester (Nicolas Cage), an Agency veteran who’s been relegated to overseeing a roomful of ancient spy machines because he once irritated some higher-ups with a program design.

Simultaneously Snowden meets in the flesh Lindsay Mills (Shailene Woodley), a photographer with whom he’d been communicating on a web dating site. She represents a liberal political perspective very different from his, but they hit it off, and their on-and-off relationship will be one of the story’s constants.

Snowden is assigned to relatively boring desk duty in Geneva, which is alleviated only when he meets Gabriel Sol (Ben Schnetzer), a snarky guy who turns him on to some unauthorized surveillance tools, and a cool CIA agent (Timothy Olyphant, looking ever more like Bill Paxton), who involves him in some actual sting operations. Those experiences sour him on the agency and lead him to resign, although he’ll continue to work with the CIA in various contract capacities—and be mentored by O’Brian—until his conscience convinces him to go rogue and purloin the data he later publicizes, using a Rubik’s cube to sneak the chip containing it past security.

Stone manages a few nice visual touches—like a scene in which O’Brian confronts Snowden via video screen, his image looming over the younger man like a threatening giant. He also puts some genuine excitement into the sequence at the end where Snowden escapes the hotel and gets past a slew of waiting reporters on his way to safety. For the most part, however, his treatment is oddly staid; even the sequence of Snowden getting the cube past guards, which should make for some chills, generates little tension.

Still, the performances are admirable. Gordon-Levitt brings low-key charm to Snowden, as well as considerable nuance. Ifans plays O’Brian—a composite figure—with a suitably icy demeanor, and Woodley manages to add a good deal of shading to a character that, on the page, comes across as bland. Cage, Schnetzer and Olyphant add some welcome color in peripheral roles, and Leo, Quinto and Wilkinson make a classy journalistic trio, though none of the parts is especially demanding. Technically the film is smoothly made—Anthony Dod Mantle’s cinematography is as generically effective as one could want, even if it lacks his distinctive flourishes, and the production design (by Mark Tildesley) and editing (by Alex Marquez and Lee Percy) are fine, if unexceptional.

“Snowden” is a conventional, respectable and slightly dull piece of work, barely recognizable as an Oliver Stone film at all. Perhaps he was wary of comparisons to the florid, eye-popping style that Bill Condon brought to the story of Julian Assange, another high-profile revealer of secrets, in “The Fifth Estate” (2013), which didn’t fare well with either critics or the public. But he might have attempted a happy mean between that degree of excess and the reverential tone he adopts here. Who’d have thought that Stone’s telling of Snowden’s remarkable story would be so unremarkable?