There’s so much that works about Catch Me if You Can that it’s easy to overlook what doesn’t. This adaptation of the 2002 Steven Spielberg film starring Leonardo DiCaprio and Tom Hanks boasts the sort of old-fashioned aspects so many contemporary musicals lack: solid storytelling, characters you come to care about and a tuneful, memorable score. Only the awkward structure and slow patches of Terrence McNally’s book prevent it from being a total triumph.

Set in the 1960s, the story relates the real-life misadventures of Frank Abagnale, Jr. (Aaron Tveit), a teenage con artist and forger who managed to steal millions of dollars in a nationwide crime spree before the age of 21. While passing himself off in a variety of glamorous occupations—including doctor, lawyer and even airline pilot—he’s being trailed by a team of FBI agents led by the indefatigable but repeatedly frustrated Agent Carl Hanratty (Norbert Leo Butz).

McNally’s principal dramatic conceit is to have Frank narrating his tale as the sort of television musical variety show that was so popular in the era in which the events take place. (Indeed, there’s a direct homage to Mitch Miller). While the format provides a natural opportunity to ogle a plethora of long-legged chorus girls going through their elaborate routines, it’s an unnecessarily distancing device that only distracts from the main story.

On the other hand, McNally’s book does an excellent job of delineating the emotional connections among the characters: between Frank Jr. and his unrepentant rogue of a father (Tom Wopat), who mentors him in the methods of misdirection; between Frank Sr. and his much younger, disenchanted war-bride wife (Rachel de Benedet); and especially between Frank Jr. and his FBI agent hunter, who turn out to be kindred spirits despite being on opposite sides of the law. Only Frank’s relationship with Brenda (Kerry Butler) a young nurse (Kerry Butler) for whom he finally decides to go straight, feels perfunctory.

Director Jack O’Brien, choreographer Jerry Mitchell and composers Scott Whittman and Marc Shaiman—reuniting after Hairspray—have created a dazzling production featuring plenty of memorable musical numbers. Co-stars Butz and Tveit each have their showstoppers, the former with the manic “Don’t Break the Rules” and the latter with the anthemic “Good-Bye.”

But each of the characters gets their moments to shine in the musical spotlight: Wopat displays his languorous baritone on such songs as the wonderful “Butter Outta Cream”; Nick Wyman and Linda Hart, as Brenda’s blue-blood parents, let loose in the riotous “(Our) Family Tree”; and Butler makes the most out her powerful ballad “Fly, Fly Away.”

Mitchell’s choreography, whether for the leggy chorines, the loose-limbed Butz or the youthfully athletic Tveit, is consistently eye-catching. And the brassy musical arrangements gives the score a wonderful, ‘60s flavored pop quality.

As the ever scheming but endearing Frank, Tveit delivers the sort of charismatic leading man turn that instantly catapults him to the big leagues. Butz is a consistent delight as the stressed-out FBI agent, investing the character with endless comic quirks that score big laughs. And Wopat is very touching as the loving father but damaged father who eventually hits the skids.

Neil Simon Theatre, 250 W. 52nd St. 877-250-2929. www.ticketmaster.com