" The Shapes of Space," the Guggenheim Museum’s spirited if sometimes disjointed display of works from its collection, might almost be titled “Welcome to the 21st Century.” Its accomplishments are several:It puts on view many of the museum’s latest acquisitions. While a 1913 Mondrian is the show’s earliest work, nearly half were acquired after 2000.It allows two young assistant curators and one curatorial assistant — Ted Mann, Nat Trotman and Kevin Lotery — to spread their wings, under the supervision of Nancy Spector, the museum’s chief curator. It shows the Guggenheim, under Lisa Dennison, its director of two years, trying to look like a museum and make active use of its collection, rather than functioning mostly as a kunsthalle dedicated to traveling blockbusters. And finally, it offers a good argument for expansion of the local kind — not in Bilbao, Berlin or Abu Dhabi, but right here in New York. That may be beyond the museum’s reach right now. But as a testament to what might be called the Thomas Krens legacy — he will be remembered as a builder of museums who failed to build where his museum needed it most — this is partly a depressing show, symptomatic of the kind of museological missteps that have become par for the course in New York. But let’s not go there. Let’s just say I sometimes found myself wondering how various works might look on level ground, as opposed to in the museum’s sloping spiral, and with fair amounts of space. There’s a healthy vitality to this array of American and European works on the theme of space — a central issue to all art, but especially modern — and it raises worthwhile questions about the changing nature of museums, even if some of the answers are more palatable than others. It points to what might be called festivalist collecting: the acquisition of large, crowd-pleasing artworks that are entertaining and irresistible on a superficial level. It also reminds us that such works offer outstanding photo-ops. The show opens on the rotunda floor with “The Shape of Space,” Alyson Shotz’s immense shimmering curtain of plastic lenses, hand-cut and stapled together, which is the source of the show’s title. From afar it suggests a giant wind chime, but mainly it is a giant magnet for cellphone cameras. Dividing and multiplying its surroundings, it provides tiny, glimmering, beveled views of the museum’s rings, Central Park, an apartment building, traffic. It even projects its own visible shield, a second layer of floating reflections that seems solid but is not. Next comes Piotr Uklanski’s “Untitled (Dance Floor),” which is in fact a dance floor: an eye-popping grid of flashing light, colors and patterns synchronized to various pop tunes of the disco and rap variety. This work was better out in the world, in its original incarnation as the floor of Passerby, the bar Gavin Brown opened in the front part of his gallery when it was on West 15th Street. According to the label, “it radically subverts the normal functions and patterns of behavior” of the museum, which is to say that it contributes to a certain mall-like atmosphere. Still, it’s not often that you can look at a Mondrian while listening to Missy Elliott. The Uklanski is actually nothing new. A nearby label accompanying paintings by the Constructivist Laszlo Moholy-Nagy mentions that that artist “began to experiment with immersive, time-based displays of colored light that viewers could literally enter” at the Bauhaus in the mid-1920s.After this the show settles down, moving back and forth in time and in its concept of space — touching on psychology, commerce, landscape, history, politics, architecture and occasionally sex. Ricci Albenda’s bulging, implicitly fleshy built-in plaster reliefs insert a warped space into the very walls of the museum. The forms — positive and negative versions of the same design — resemble cartoonish versions of the Guggenheim’s architecture. (Bugs Bunny could come bouncing out.) But they are also somewhat female, which fits the museum’s womblike structure. Along the floor next to the Albendas, an unusual fluorescent-tube sculpture by Dan Flavin that curves out from the wall looks skeletal, like a bit of spine.There are numerous other moments of interesting cross-pollination. Elliott Hundley’s feather-light collage-assemblage seems like a compression of Pipilotti Rist’s immense installation, “Himalaya’s Sister’s Living Room,” an onslaught of the furniture, periodicals and bric-a-brac of everyday life (with photo murals) punctuated by short, hallucinatory videos. In one bay, a Robert Gober sculpture and a Lee Bontecou relief are united by an emphasis on orifices and craft and a predatory air. In another, a work by Tom Friedman (chicken wire and painted foam pellets) communes about molecular structure with two early mobiles by Alexander Calder. There is both a comfort and an excitement in seeing continuities reach across generations and mediums. Louise Bourgeois’s “Cell V,” with its circle of weathered French doors tightly enclosing two immense wood balls, demurely communicates domestic confinement, monstrosity and fecundity, feelings that run rampant in Mika Rottenberg’s “Dough,” a few yards away. There the viewer enters a small, confining room to watch a video of an immense woman, the queen-bee center of a small, confining factory turning out large clumps of dough. Historic space is given a feminist twist in Aleksandra Mir’s sly video “First Woman on the Moon,” which shows the artist planting a flag on a bit of Dutch soil that has been temporarily refashioned by bulldozers to resemble the moon’s surface. The proceedings are enhanced by Peter Viberg’s “Echo of Space” (1984), which mingles a mishmash of music — triumphal, New Age, romantic-comedy — with the familiar broadcasts of the actual lunar landings. Not everything works. A Lucio Fontana slash painting seems perfunctory; there must be more exciting ways to account for the way pictorial and actual space merged in the 1960s. Some of the recent acquisitions are too flimsily fashionable (Liam Gillick, Walid Raad) or too generic (Maria Elena González). At the top of the show, Rirkrit Tiravanija’s “Untitled 2002 (He Promised),” a chrome and stainless-steel version of a house in Los Angeles by the modernist Austrian architect Rudolf Schindler, seems like an expensive boondoggle, and a not very well-made one at that. Matthew Ritchie’s immense wall painting “The Hierarchy Problem” suggests the haywire incomprehensibility of space, both mental and outer, but would make more sense if it were presented with the components of the immense four-part installation of the same title.Or maybe it shouldn' t be confined to the curved wall that narrows the museum’s top ramp to the width of a corridor. In the main, the curators have made the most of a difficult situation. But one thing to be avoided in an exhibition about space is the appearance of running out of it.