Robert Altman, the grizzly-bear genius of American cinema celebrated in the new documentary Altman, first found success at the same time as Steven Spielberg, George Lucas and Martin Scorsese, but he was no movie brat. With a career in television and a spell as a fighter pilot behind him, he had a jump of nearly 20 years on those upstarts by the time he achieved his breakthrough in 1970 with his fifth film, the spiky Korean war comedy M*A*S*H, made when he was 44. Over a 50-year period, he bashed out almost 40 films. There were iconoclastic assaults on genre (the anti-western McCabe and Mrs Miller, the wayward detective film The Long Goodbye, the who-cares-whodunnit Gosford Park), sprawling ensemble pieces (Nashville, A Wedding, Short Cuts) and dazzling anomalies such as the psychological mystery 3 Women, the Hollywood satire The Player, the musical Popeye and the jazz thriller Kansas City. He broke the mould after every movie.

These superficially dissimilar pictures shared key traits: slow, inquisitive zooms from multiple cameras, improvised scenes that strayed far from the script (“Good disintegration!” Altman would tell his cast approvingly). Then there was his greatest innovation, the tiny microphones picking up dialogue from each actor, that Altman then mixed together into dense, overlapping ambient noise. The word “Altmanesque”, though, evokes more than just a style. It’s a sensibility: anti-establishment, individualistic, raucous, humane.

Even those who have seen none of his films will have felt his impact. It resides most obviously in the work of Paul Thomas Anderson: Boogie Nights, Magnolia and Inherent Vice are virtual cover versions of Altman. “I’ve stolen from Bob as best I can,” admitted Anderson, who later dedicated There Will Be Blood to him. The influence also extends to Richard Linklater, Alejandro Gonzáles Iñárritu, Judd Apatow, Noah Baumbach and Michael Winterbottom, none of whom would be making quite the same films had Altman not preceded them. Even Downton Abbey, conceived by Gosford Park’s screenwriter Julian Fellowes as the “child of Gosford”, would not have existed without Altman. Well, there had to be a downside, a cloud to offset all those silver linings.

Elliott Gould in The Long Goodbye. Photograph: Sportsphoto Ltd/Allstar

Despite the regard in which he is held by younger film-makers, there is still the danger that Altman could fall off the radar of modern cinema audiences. That’s one reason to welcome the new documentary, made in collaboration with Altman’s widow Kathryn Reed Altman, even if it doesn’t do more than provide a précis of his career. “If people come away wanting to watch Bob’s movies, then I did my job,” says its director, Ron Mann. “He’s America’s greatest film-maker. His work matters more than ever now because it stands in contrast to all the sequels, the comic-book adaptations, that Hollywood makes to sell lunchboxes.”

Sitting beside him, lips pursed, is Kathryn, who is in her 90s and was married to Altman for 46 years. I ask what daily life was like for the wife of such a prolific director. “Hard but great,” she sniffs. “Never boring.” She tells me about a trip to Cannes in 1970, where M*A*S*H won the Palme d’Or. “He was the golden – well, not ‘boy’. Golden something. Everyone was all over him but even though he was there with M*A*S*H, he had moved on. It was all one long movie to him and he just wanted to discuss his next picture.” That was Brewster McCloud, which gets Mann’s vote for Most Underrated Altman Movie. “He could have done anything after M*A*S*H,” Mann says. “So he does this far-out little film with unknown actors about a boy with a bird fixation. That’s so him.”

Mann’s documentary is weirdly lopsided. Home-movie clips are included for no reason, it seems, other than to take the edge off some of the comments by Altman’s son Stephen about his father’s absences (“For the most part, we were not his priority”). I ask Mann about this discordant note and he passes the question to Kathryn. “Stephen rues the day he said that!” she huffs. “Bob was a very devoted parent. We were always on location with him. Every summer vacation the kids were on set.” There is certainly plentiful footage here of Altman’s baby grandson, at the expense of anything on collaborators such as Shelley Duvall, Warren Beatty or Elliott Gould. A negative TV rant against Popeye by a forgotten nobody of a reviewer takes precedence over the glowing critical notices the director received for other films; it’s as if Mann is trying to reframe Altman as even more of an outcast than he really was. Meanwhile, an excerpt from Nashville manages to deliver an almighty spoiler for anyone yet to see that film.

Gosford Park. Photograph: Sportsphoto Ltd/Allstar

Mann hauls fine actors before the camera to provide nothing more than a definition of the term Altmanesque. “Kicking Hollywood’s ass,” says Bruce Willis. “Expect the unexpected,” offers the late Robin Williams. What a waste when there are so many illuminating stories waiting to be heard. “Altman was a genius,” Clive Owen tells me. “Unbelievable. I remember seeing him bleeding together some of the scenes on the set of Gosford Park. It was like watching someone compose music. A memo had gone out – ‘Everyone will be called every day, you’re all going in to hair and wardrobe, you may well be released at lunchtime, but you need to be there in case Bob wants to bleed you into something.’ He was doing one of those big scenes, bringing people in gradually, layering and layering, it was so fluid. Then, after one rehearsal, he said: ‘We’re gonna go for this now. If you know what you’re doing, we won’t notice you. And if you don’t, we will.’”

Gosford Park, with its intersecting plotlines and apparently neverending dramatis personae, provided Altman with the sort of disarray in which he felt most at home. Should things settle down, he simply shook them up again. “We were doing a scene,” Owen recalls, “and he said: ‘Stop. Actor says line, actor says line. Nightmare.’ So he sent Derek Jacobi through the middle of the scene, chasing a dog or carrying a tray or something, just to mess up the neatness of it all. I’ve worked with directors who, if you put more than a few people in a scene, they’re like: ‘How am I gonna do this?’ Now look at Gosford Park. Twenty people in a room, each with their own thread, and it looks like he just happened to catch it all. It takes an amazingly smart brain to do that.”

Neve Campbell chose Altman to direct The Company, a dance movie she had originated, for precisely this reason. “It needed to be immersive and that’s why I wanted Bob,” she says. “No other director has ever been able to capture the world in all its noise better than him. He had more fun directing 80 people than four. You never knew when you’d be on camera – with Bob you had to be on and trust he was going to find the good moments. All the safety of screen acting was gone. But that’s great for actors. Film can get boring. Much better to have someone like Bob who says: ‘OK, we’re doing this in one take, it’s a three-page scene and we’re not cutting.’” James Franco also starred in The Company. “What Altman did was make you feel like you’re not being directed at all,” he reflects. “It’s still baffling to me. It’s a bit of an art. It seemed like he was doing so little.”

M*A*S*H. Photograph: Sportsphoto Ltd/Allstar

Maya Rudolph remembers fondly the atmosphere on the set of Altman’s 2007 swansong, A Prairie Home Companion, on which her partner, Paul Thomas Anderson, served as backup director for insurance purposes. “Bob loved people coming up with stuff,” she says. “I was playing a stage manager, so I got to be in everything, to be in every room, yet still to be sort of on the outside of it. You get to watch someone like Kevin Kline, who’s the perfect example of a skilful improviser; Bob would encourage him to improvise and do more and we’d just watch him fly, coming up with all this insane, hysterical physical comedy, none of which was in the script. You’d always hear Bob say: ‘Ah, that’s great, let’s keep going.’ There were multiple cameras moving all the time, and everyone was mic’d at all times; he loved that organised chaos. Being with him was like being at the most fun party ever, with the best host.”

Altman, the documentary, may be flawed in its appraisal of Altman, the director. But there’s no doubting Mann’s personal connection with the work. (Though the two film-makers never actually met, both served on the advisory board for the National Organisation for the Reform of Marijuana Laws.) “What I love about Bob is that there’s no way you can label him,” he says. “Everything you can prove can also be disproved, so that you can never say definitively what an Altman film is. They say he didn’t like writers but just look at [the 1974 crime drama] Thieves Like Us, which was a very faithful rendering of Joan Tewkesbury’s screenplay. They say he was an ensemble film-maker but look at Secret Honour [the 1984 one-man movie about Nixon]. It’s just one actor, Philip Baker Hall, in a room.”

There is, Mann concedes, one aspect about which there can be no dispute. “He reinvented the language of cinema. And he made the films he wanted to make. Sometimes it worked, sometimes it didn’t. But he used to tell students: ‘If anyone tries to mess with your movie, burn the negative.’ He was always uncompromising in that way.”

Altman is released in the UK on 3 April