Jim Jarmusch, the “quirky” (he hates the word) Manhattan filmmaker, has been getting some good press recently. But judging by the fawning profile of him that ran recently in the New York Times Magazine, I wonder if the cinephiles admire him more for his integrity and independence as a filmmaker than for the actual films he makes.

We all have critical blind spots, and Mr. Jarmusch may be one of mine, but I’d like to strike a note of skepticism about his much-heralded “Broken Flowers,” opening today. It won the Grand Prix (second prize) at Cannes this year, and, though I wasn’t there, I find it just a little hard to believe there wasn’t more than one better movie in competition.

Not that it’s bad or a waste of time. Heralded as a departure from such self-consciously arty and serious predecessors as “Night on Earth” or “Dead Man” by being comic and more accessible to a popular audience, “Broken Flowers” seems to me a bit of a bore. Not only does it have little of interest to say, but it’s only occasionally funny – usually a handicap for a comedy, though perhaps not if you’re independent and “quirky.”

As in nearly every film he appears in, Bill Murray is the chief attraction. He plays an aging Don Johnston called Don Juan (or possibly the other way around) who receives an anonymous letter from a supposed former lover telling him he has a son who is now 18 and possibly in search of his father.

Rather than wait for the son to come to him, Don narrows down the potential mothers to four and goes off to interview them – though he hasn’t seen them in years – in hopes of finding out more. A fifth ex-girlfriend from the appropriate period has recently been killed in a car accident.

Actually, the ex-girlfriend tour is the inspiration of Don’s neighbor and friend, Winston (Jeffrey Wright). It is not Don’s idea to take the initiative. Don doesn’t take the initiative about much of anything. Having made enough money in computers to retire, he likes to sit, or lie, on his nice leather couch and look at television. Or at nothing. The film opens with him watching “The Private Life of Don Juan” with Douglas Fairbanks Sr. (1934) on television, as his latest girlfriend (Julie Delpy) is in the process of leaving him.

Mr. Jarmusch is already a man who likes long takes, long silences, and tableau-like scenes, while Bill Murray has in recent years made rather a specialty out of the meaningfully silent stare. Obviously the two were made for each other. But you could also say that each over accentuates the other’s cinematic tic, making the whole film seem mannered. The long takes are meant to betoken a profundity that the material too often isn’t able to back up.

Winston is not a character of much intrinsic interest. He’s only there as a personification of Don’s energy, curiosity, and drive, which the film cannot do without but are otherwise absent. He makes up Don’s itinerary and all his travel arrangements and even gives him a CD with music to listen to on the road. Why Don meekly does what Winston tells him without any apparent interest of his own in what he might find remains obscure.

The first ex-girlfriend is Laura (Sharon Stone), a trailer-park queen with a daughter aptly named Lolita (Alexis Dziena). She is the widow of a race-car driver (“Larry exploded in a ball of flames; now it’s just me and Lo”) who is only too glad to see Don turn up on her doorstep – though no gladder than the sultry Lolita.

Next comes Dora (Frances Conroy), a real estate agent who seems almost as catatonic as Don himself. She is followed by Jessica Lange as Carmen, an “animal communicator” with little time to communicate with Don. This segment is meant to be satirical, I think, but the only really funny thing is a scene-stealing performance by Chloe Sevigny as Carmen’s bitchy assistant.

Penny (Tilda Swinton) is even more downwardly mobile socially than Laura and even less disposed to speak to Don than Carmen. Her knuckle-dragging boyfriend (Larry Fessenden) accuses him of being impolite and knocks him out. When he wakes up he goes to the grave of the dead ex-girlfriend and weeps, briefly, in the rain.

Dora’s bit is the best of the film. As she is engaging in a sort of competition with Don to see who can appear more affectless, her husband Ron, played by the wonderful Christopher McDonald, breezes into the room and invites Don to stay for dinner. “Really, I couldn’t,” Don says. “Sure you could,” Ron says. Soon the three of them are seated around the antiseptic dining-room table of Ron and Dora’s show house, talking about moneymaking opportunities. “One day water will be more valuable than oil, than gold,” Dora says.

“If you need a drink,” Ron adds, “you’re not going to take a swig of oil. Or gold.”

“You got that right,” Don says.

It’s a bit minimalist, like everything else in the picture, but still quite funny, and it leads nicely into what promises to be a meditation on time and commitment and identity. Ron goes to get an old photo of Dora in which she appears as a young hippie chick. Don whispers: “I took that photo.”

Dora, in her zombie-like way, says: “Strange how people’s lives change.”

How true! Yet in spite of a brief reprise near the end, the theme never quite manages to emerge as anything more interesting than some such banality as this. Maybe I just can’t see it.