Nobody loves the Rolling Stones as obsessively as Martin Scorsese. Think about the way Mick Jagger’s spastic shrieks on “Monkey Man” captured the paranoid craving of the cocaine-addicted mobster Henry Hill (Ray Liotta) in “Goodfellas.” Or the fateful way the guitars of “Gimme Shelter” shimmer like an elegy over the graves of dead Irish cops in “The Departed.” Mr. Scorsese’s 1995 film “Casino” even used two separate versions of “Satisfaction” to mark the passage of time. Through the years, the director has repeatedly made freshly iconic use of the band’s classics, usually to ramp up the visceral impact of key scenes, but also to remind us how edgy and spookily relevant the Stones once were.

So it’s hard to tell if Mr. Scorsese intends “Shine a Light,” his two-hour concert film of the band’s 2006 performances at New York’s Beacon Theatre, as a repayment of psychic debts or a prosperous fanboy’s act of generosity. Individually, the deathless guitarist Keith Richards and that rooster sophisticate, Mr. Jagger, are pop-culture avatars for the ages. Collectively, however, the Rolling Stones haven’t mattered to anyone but their accountants in roughly three decades. Excitement at news that Mr. Scorsese was at work on a Stones project quickly diminished with the realization that “Shine a Light” was mostly to consist of contemporary concert footage. The group commissions such things to document every tour. Back in the glory days, this sometimes made for unexpectedly dangerous filmmaking, namely the Maysles brothers’ epochal “Gimme Shelter” (1970), which placed the Stones at the epicenter of the death of the ’60s, and Robert Frank’s outlawed “Cocksucker Blues” (1972). In 1968, Jean-Luc Godard ventured into the studio to film the recording of “Sympathy for the Devil,” and Mr. Jagger brought his squirrelly zeitgeist to Nicolas Roeg and Donald Cammell’s dramatic feature “Performance” (1970). So why, exactly, did a filmmaker of Mr. Scorsese’s significance want merely to produce more fodder destined for suburban American home-theater systems?

Maybe because it was the only way he could be sure of catching a really great Stones gig — at least, as great a Stones gig as the band is likely to put on these days. Mr. Scorsese frames the event as a work-in-progress, turning the camera on himself as he frets over what songs the band will select for its set list and giving a himself — as the borderline manic “Marty” we see on American Express commercials and in guest shots on “Curb Your Enthusiasm.” There’s a humorous prelude of Mr. Jagger, sitting on a jet, picking apart Mr. Scorsese’s lengthy, compartmentalized lists of songs for their shows, with an air of flippant self-regard that always has been a keynote of the singer’s persona.

It’s not clear if the director intends his own presence as an homage to all those great Stones documentaries devoted to “the process,” or if he simply wants to convey his epic adulation, but once the show starts, it’s pretty obvious that this is the Stones as Mr. Scorsese most wishes to hear them. Only one song that appears in the film was recorded after 1978 (that being “She Was Hot,” from the forgotten 1983 album “Undercover”). Aside from four selections off of 1978’s “Some Girls,” in fact, everything dates to 1972’s “Exile on Main St.” and earlier. Many are songs that accompanied whackings or wedding scenes in Mr. Scorsese’s films. Those choices alone redeem the effort. In a nutshell, this is the Rolling Stones show you’ll never get to see in person, because it’s liberated from all the crappy material the band has released in tandem with the Enormo-Dome tours it launches every three years or so. Even so, “Shine a Light” ultimately remains a curiously high-end commodity rather than an incisive backstage saga like “The Last Waltz,” Mr. Scorsese’s 1978 farewell to the Band that is counted among the better music documentaries. Between the songs, which consume roughly 90% of the two-hour running time, the screen lights up with vintage newsreel clips of interviews that emphasize the Stones’ commitment to their own longevity.

At first, an early-20s version of Mr. Jagger implies that he can only imagine the band making it through another year. Perhaps a decade later, he tells Dick Cavett that he has no problem with being onstage at 60. Meanwhile, a similar series of flashbacks gives us a progressively dissolute Mr. Richards suggesting that his survival is largely due to his not worrying about such things. And — bang! — the camera is back onstage, drinking in every crevice, rut, and tributary carved into the guitarist’s notoriously, gloriously ruined face: a face to stare down the Reaper and send him packing.

Mr. Richards, and his slashing interplay with the Stones’ second guitarist, Ron Wood, is the constant, alchemical element that keeps “Shine a Light” interesting — that is, until whatever point individual members of the audience begin to experience eye and ear fatigue. Mustering a small army of first and second cameramen and lighting technicians, Mr. Scorsese has opted for an annoyingly kinetic visual approach in which the camera, at any given moment, seems as one with Mr. Jagger’s forever wiggling butt. Just to amuse myself, I counted off the seconds between cuts from one shot to the next. Rarely did I get past “three.”

Mr. Jagger, whose fascinating elastic face, as ever, threatens to morph into that of Don Knotts as “The Incredible Mr. Limpet,” is typically as erratic as drummer Charlie Watts is stalwart. The tight frames often overly emphasize how baldly theatrical he is, affecting broad facial gestures that are drained of his bandmates’ collegial spontaneity. There’s also the matter of his engagement with the songs. He’s more likely to chew up or throw away lyrics than to really sing them, even when he’s sharing the spotlight with guest vocalist Christina Aguilera, who out-belts him on the once-salacious “Live With Me.” Invited to fulfill the old Tina Turner-Merry Clayton soul-shouter role, Ms. Aguilera also marks a nod to the current pop moment. By way of thanks, Mr. Jagger gropes her from behind. (Two other guests, White Stripes guitarist Jack White and blues giant Buddy Guy, escape unscathed).

The singer is most thrilled when he’s doing songs from the discoinfused “Some Girls,” which briefly restored the group’s edge in the late 1970s, as Mr. Richards appeared on the verge of incarceration for drug charges. There’s something hilarious about the line “This town’s in tatters,” in reference to today’s building-boom Manhattan, especially when it’s sung at a charity benefit concert presented by President Clinton. The old-fashioned misogyny of “Some Girls” feels more accurate to Mr. Jagger’s experience. The way he spits out the words implies a lingering distaste for alimony, lawyers, and gold diggers, though — oddly —one particular racially charged line has been edited out of the performance, presumably for reasons of political correctness. (The horror!) But that’s not so much a disappointment as an obvious missed opportunity. Why not invite President Clinton to join in on a verse or two? Given the song’s context, the ironies would be delicious.