Colman Domingo as Ralph Abernathy, David Oyelowo as Dr. Martin Luther King, Jr., André Holland as Andrew Young, and Stephan James as John Lewis in a scene "Selma," which has been the subject of controversy over the last week. (Atsushi Nishijima/AP)

‘Will this ever end?”

That’s President Lyndon Baines Johnson speaking to an aide early in “Selma,” Ava DuVernay’s stirring, ambitious drama about Martin Luther King Jr. and the voting rights movement of 1965.

In the movie, Johnson — weary from having passed the Civil Rights Act of 1964 — is talking about King’s push for a federal law protecting blacks’ right to vote. But he could just as well be talking about the controversy that has engulfed “Selma” since its release on Christmas. No sooner had critics (this one included) given the movie rapturous reviews than the fact-checkers began to descend, in a ritual as time-honored as the swallows returning to San Juan Capistrano.

The Gotcha Game has become as reliable a feature of awards season as red-carpet gaffes and snits about snubs. But as “Selma” has been put through the wringer in the past couple of weeks, the ritual is wearing thin. What’s more, it has taken on the tiresome contours of a Manichean choice: You’re either on the side of art or on the side of truth; gauzy poetic license or cold, hard facts. If you admire “Selma,” you are perforce being unfair to Johnson’s legacy. If you think DuVernay has taken too many liberties with chronology and characterization, you play into the age-old habit of preferring your civil rights stories delivered by way of a white savior — like the heroic FBI agents in “Mississippi Burning” or plucky Emma Stone in “The Help.”

Thanks to a burgeoning population of historians, book-flogging authors and TV-ready firsthand witnesses, a ubiquitous social media culture and a voracious 24/7 news cycle, the fact-checking-industrial complex is clearly well entrenched. “What X Gets Wrong About Y” is a format as irresistible to click-happy Web sites as sex listicles and Kardashians.

But if the Gotcha Game is here to stay, we can at least agree on some new rules. And we can begin by adjusting our own attitudes toward fact-based films and their inevitable nit-pickers. Rather than the dualistic one’s-right-one’s-wrong model, it behooves audiences to cultivate a third eye — a new, more sophisticated way of appreciating both the art and the reality that inspires it.

Plenty of movies this season are amenable to third-eye viewing: “Unbroken,” Angelina Jolie’s hugely successful adaptation of the book about World War II hero Louis Zamperini, is catching flak for giving his spiritual journey short shrift. “The Imitation Game,” about the British codebreaker Alan Turing, isn’t gay enough. “Foxcatcher,” about wrestler Mark Schultz and John E. DuPont, is a little too gay.

But by far the most distressing push-back campaign has been aimed at “Selma,” in which Johnson appears as an important supporting character, cajoling, bullying and horse-trading with King over timing and tactics of the voting rights legislation they both supported. As portrayed in galvanizing performances by David Oyelowo and Tom Wilkinson, these two canny political players emerge as fascinating, often contradictory characters, one whose genius lies in grass-roots activism, the other in Washington ­realpolitik.

To those who watch and listen to “Selma” carefully, they’ll realize that Johnson isn’t presented as the story’s villain. Far from it. In one of the movie’s opening scenes, he tells King he wants to help with voting rights but feels the timing is wrong. Later, forcefully pushing back against King’s sense of urgency, a frustrated Johnson barks, “You’ve got one problem, I’ve got 101,” graceful shorthand for the myriad political constituencies and competing interests he was juggling behind the scenes. His speech to Congress proposing the Voting Rights Act of 1965 — when he famously quoted from the civil rights anthem “We Shall Overcome” — is one of the most affecting moments of the movie.

Such high points were obviously lost on Johnson historian Mark Updegrove and former aide Joseph Califano, who have taken DuVernay to task in recent weeks for unfairly portraying LBJ as an opponent of King’s, when they were actually allies. Even Andrew Young — who is a character in the film as a young member of the Southern Christian Leadership Conference — has said that “Selma’s” depiction of Johnson “was the only thing I would question in the movie. Everything else, they got 100 percent right.”

When debates such as this arise — and they do, inevitably — viewers are caught in the crossfire. One can see “Selma” as a great cinematic and cultural achievement, a galvanizing portrait of an era and a movement that have never gotten their due in theatrical feature films. But it’s also important to understand and respect the writers, historians and firsthand witnesses to the events who have found watching “Selma” disorienting, if not disturbing. I especially regret that an edit in the film erroneously suggests that Johnson ordered FBI Director J. Edgar Hoover to send incriminating tapes of King’s alleged infidelities to the activist’s wife, Coretta. If I had a wish for “Selma,” it would be that DuVernay could have found another way to solve a structural problem — getting from the White House to the King residence and the tapes — without inviting that inference.

But that artistic choice doesn’t negate all that “Selma” gets right — most of which has less to do with strict adherence to the facts than with stirring images, riveting drama and authentic, deep emotion. It would be a shame if viewers are put off from “Selma” by the debates swirling around it, instead of allowing those conversations to inform a rich, emotionally powerful and uncannily timely cinematic experience.

How to reconcile facts and feelings, art and fealty to the truth? When filmmakers recall with pride about the deep reporting and research they’ve done for their projects, then they deserve to be held accountable for their projects. For fact-based films, accuracy becomes a formal element, along with acting, design and cinematography. It’s up to each viewer to identify the threshold where artistic license compromises the integrity of the entire endeavor. Cinema has more responsibility in this regard precisely because of its heightened realism, its ability to burrow into our collective consciousness and memory, where the myth has a tendency to overpower settled fact.

But viewers have responsibilities, too. If accuracy has become a formal element of historical dramas, then the ensuing fact-checks have become just as integral a part of how we view them. That means it’s incumbent on audiences to engage in a mode of spectatorship that, rather than decide who’s right, can listen to and respect expert critiques, and still open themselves up to a piece of filmed entertainment that speaks to less literal, more universal truths.

The correct question isn’t what “Selma” “gets wrong” about Johnson or King or the civil rights movement, but whether we are sophisticated enough as viewers and thinkers to hold two ideas at once: that we’re not watching history, but a work of art that was inspired and animated by history. That we’re having an emotional and aesthetic experience, not a didactic one. That the literalistic critiques of historians and witnesses can co-exist — fractiously, but ultimately usefully — with the kind of inspiration, beauty and transformative power that the very best cinema such as “Selma” can provide.

The Gotcha Game isn’t going away anytime soon. The trick is making sure that it isn’t zero-sum.