It takes a Serbian or at least a Balkan familiarity to understand and enjoy many of the situations, characters and jokes of 'Zavet' as well as of many other films of Kusturica. See for example the opening scenes, with the remote village in the Serbian mountains, with the low-tech devices that defend the integrity and way of life of the inhabitants, the nostalgia for the good days of the Communist rule, and the awakening of the young brat watching his nude teacher at the sounds of the Soviet hymn. Kusturica not only tries to depart from the tragic history of Serbia described in his previous movies, but creates a whole world of himself in the process.
This is not a political film or not an explicit political film in any case. It's a fun film before all. Kusturica creates a set of characters that we care about. Music plays an active role in this film same as in all his other movies. His style is direct and grotesque, we now what he feels about his characters and we know that he wants us to feel the same. The space he develops melds present, history and magic, and the colours seem to be of a Douanier Rousseau of modern cinema.
This is not a perfect film either. The principal flaw is the length, some editing and shortening would have been useful, as at some point in time the director seems to have run out of ideas and repetitions show up. It is yet one of the most catching, amusing, moving films that I have seen lately.

(I'll indicate in this review the point where spoilers begin.) My dissatisfaction is split: 30% tone-deafness, 70% lackluster writing.
The 30%: I agree with the first commenter's synopsis about the lack of diversity in the characters and scope of the stories. I was surprised how, this film, at best, woefully shortchanges the real NYC by presenting a collection of people and relationships so narrow as to come across as if it's inhabited only by the cast of Gossip Girl (this is coming from someone who likes Gossip Girl). A few minority characters are written into the stories, but they are included by obligation, while we can see the gears under the film so clearly, striving to "be diverse" but falling ever-so-short.
The 70% is why everything falls short. All characters, white plus a few token minorities, are one-dimensional, cardboard cutouts of people concepts. Worse, their interactions with each other are scripted in such a way that for each vignette in the film the audience is treated to what I'd say is a "gag": we get a basic conceit, then some punchline intended to be a clever twist. But even if we suspended cynicism for a moment to say, "Okay, that was a surprise"...the stories are still not that interesting, because they, too, are shallow. When you fashion stories so that their existence hinges solely on the unexpectedness of the ending, you're writing jokes.
Spoilers below...
The movie primarily tries to tell romantic stories. That's fine. But romance is amazing, deep, sometimes complex. These "romantic" stories each feature a girl and a boy who at some point share the same location and get to look at each other. Words exchange, thoughts are projected through voice-over, but they too only manage to communicate to the audience merely that one person is attracted to another.
Meaning, there is no seduction (in the broad sense), no tension, and neither confrontation nor communion between the wills of two different people trying to reconcile their existence to accommodate the Other. The only story involving a superficial "seduction" is told just so the audience ends up being surprised that the guy (Ethan Hawke) gets outwitted by the girl he's hitting on, who unexpectedly turns out to be a hooker. Sure, his words when trying to pick her up are interesting to hear and we are amused as we'd be if we were next to them, but there is nothing of substance to this story outside of "A then B". So it unfolds, if something like a postcard could "unfold", with all the other tales as well: A then B--That's It, the only point being that these happen to occur "on set" in Manhattan. By the way, the only Brooklyn we see is the Coney Island sketch; the only Queens is the flickering of a train ride taken by a character traveling to the West Village.
It's easy to pick at movies that play into all the common stereotypes of race, gender, sexual orientation, and so on. _New York, I Love You_, however, deserves to be held to stricter scrutiny because of its title. We expect to see the real New York, and real New Yorkers, but instead we have paraded before us the selected slice of a demographic, its characters flown in from The O.C., plus a few others to make it SEEM as if we are paying attention to diversity. But when we look closer at who those characters are, the whole sham becomes an affront to the very notion of diversity and the ethnicities and cultures the movie shamefully fails to represent.
For example, the story with the Latino man with the little white girl in the park, who gets mistaken by two ladies as her manny (male nanny) when in fact he's the father. Notwithstanding the last scene of this part was unnecessary from a dramatic-construction point of view (it would have been far more interesting to end it when the mother and boyfriend/stepfather are strutting the girl away), it is frankly a bit disgusting that the scene where we learn for sure that the girl's father is Latino ALSO must inform us that he is a sexually desirable dancer. What, the dad can't be just some guy from South America? Now that he's obviously hot, is the audience better prepared to accept that he had a kid with a middle-to-upper-class white woman? Are we that naive as to require such? As if a Mexican construction worker would obviously be too unpalatable.
It's not my place to dictate where the movie should have gone. But in every conceivable set-up and plot twist, the direction taken screams status quo, appeals to safety. All these stories could have been made more interesting, even if we were forced to keep the single-dimensionality of the characters inhabiting them, at the very least by not choosing from standard and obvious stereotypes. Asian girl living in Chinatown being leered at by a scraggly old white guy? How 'bout an Asian cougar pursuing a white college kid instead. Again, I'm not saying the entire conceit has to be changed. It's just that every. damn. story premise. is so hackneyed--and thus they fail to convey anything about why one might love New York, outside the trite. The real way to have improved the film would be to have written a script worth reading.
I will concede the pleasantness of the soundtrack, the good pacing of the movie (even if what was being paced was, well, dredge), and the general feel of many of the scenes. The movie was just fine to sit through, and I wouldn't dissuade anyone from doing so. However, it is telling that the most significant homage paid to non-superficiality is when the old opera singer says (paraphrased) "That's what I love about New York: everyone's from a different place." Well, you wouldn't know it from watching this one.