More than one review of The Grand Budapest Hotel likens Wes Anderson’s new movie to a Russian nesting doll – a tale within a tale within a tale. It is 1985 and an old writer (Tom Wilkinson), famous throughout the fictional central European country of Zubrowka, recounts a story of 20 years before, when as a younger man (played by Jude Law) he stayed at the titular hotel. He strikes up a conversation with its owner (F Murray Abraham) who proceeds to tell another story, about his time working as a lobby boy there apprenticed to the hotel’s famous head concierge, Monsieur Gustave (played by Ralph Fiennes). In this story, the year is 1932, a time of European anxiety and cosmopolitan sophistication between the wars. The nesting-doll imagery is apt because the intricately built plot opens up in layers. And the analogy suits the film’s visual aesthetic too, right down to the filmmaker’s fondness for hand-painted flourishes and the sense that the players are employed as movable puppets.

But to fully understand The Grand Budapest Hotel you need to look right inside the dollhouse and a viewer would do well to pack a small kit of handmade precision tools. My suggested checklist includes a scrapbook, a pair of tweezers, a magnifying glass, a telescope and a stethoscope.

The scrapbook is for collecting fabric swatches of some of the Texas-born filmmaker’s most beautiful textures and colour palettes, always a key element in his storytelling and character development. The nuances of young Max Fischer’s insecurities and pretensions as a precocious student at Rushmore Academy in Rushmore (1998) are sewn into the red beret worn by Anderson’s regular collaborator Jason Schwartzman; the pluck of the title character in The Fantastic Mr Fox (2009) is woven into the corduroy and tweed of the fellow’s little clothes. (The fabric and, indeed, the cut of his garments mimics that of the idiosyncratic wardrobe favored by the film’s creator himself.) And Monsieur Gustave’s crisp, stylish lapels hint at a romantic flair, with dashes of sexual insouciance, criminal ingenuity and political bravery thrown in, too.

The tweezers in our toolkit are useful in all sorts of ways. For one, they allow the examiner to pick up something as delicate as a background prop in a scale-model submarine created for The Life Aquatic With Steve Zissou – maybe a crinkled old photograph hanging on the hull or a monographed life-preserver – without upending all the other tiny parts in the frame. The fine grip is useful for prying apart small pieces of the film’s construction to see how the mechanism works, how individual parts affect the whole. Delicate work, indeed, because how can you remove any element of Moonrise Kingdom’s extended ensemble without also diminishing the loveliness of its central romance between Sam (Jared Gilman) and Suzy (Kara Hayward)? All the narrative components are intricately interlocked in a Wes Anderson assemblage – even Moonrise Kingdom, with its tight focus on adolescent love, depends on the wide-angle context of an entire island community for resonance and relevance. The tweezers are needed to probe the fine details of a directorial universe that’s simultaneously concerned with a close-up view and the big picture.

And that is exactly why we also need a magnifying glass. Wes Anderson is a maker of biodomes, dioramas, terraria, model villages and bible scenes carved on a grain of rice. Even when he’s taking an epic, wide-angle view, whether set on a train chugging across India in The Darjeeling Limited or beneath the sea on a research vessel scoping out a mythical Jaguar Shark in The Life Aquatic, charm is in minute details that beg for enlargement. These can be charming or alienating according to your taste: like coriander, the strong flavour of a Wes Anderson film tends to divide viewers into fans and not foes exactly, but certainly the uncharmed.

The magnifying glass is useless though without a telescope kept at hand, because these movies are simultaneously tiny and sweeping in narrative. A lot happens in an Anderson fairy tale – crossing countries, seas, school years, and lifetimes. The Grand Budapest Hotel is the filmmaker’s most epic story yet, embedding the real pains of mid-20th-Century war, fascism, communism and immigrant displacement in a story of fabulous preposterousness. There’s no way to take it all in without a lens that accommodates the long look. Same thing goes for assimilating the grand ensemble casts that participate in every project. Other visitors to this grand hotel include characters played by Tilda Swinton, Edward Norton, Adrien Brody, Willem Dafoe, Jeff Goldblum, Saoirse Ronan, Mathieu Amalric, Bill Murray, Harvey Keitel, Owen Wilson and – of course – Jason Schwartzman.

But do these characters exhibit heartbeats? That is the question. Cue the stethoscope! The strength of the pulse and with it, a sense of the filmmaker’s compassion for his characters, makes all the difference between a Wes Anderson movie that moves and one that keeps the audience at arm’s length. His films succeed most when he creates his characters from the inside out rather than the outside in, – when he lets his characters flounder a bit, expressing human emotions rather than disappearing into drollery, stylized responses, and hand-embroidered furnishings. In what category should one place The Grand Budapest Hotel? The answer will vary from person to person. What is so rewarding about a Wes Anderson film, though, is that even when it appears to slip into the second category, your instrument may still detect exquisitely subtle thrums of life.

If you would like to comment on this story or anything else you have seen on BBC Culture, head over to our Facebook page or message us on Twitter.