Armie Hammer and Leonardo DiCaprio as the younger Clyde Tolson and J. Edgar Hoover in "J. Edgar."

Here’s the thing: It’s hard to follow a story when the people telling it look like Mr. Potato Head.

Petty as it may seem, that’s one of “J. Edgar’s” major problems. In an attempt to make the incredibly attractive actors Leonardo DiCaprio and Armie Hammer (“The Social Network”) look like the not-so-incredibly-attractive and much-older J. Edgar Hoover and Clyde Tolson (Hoover’s closest colleague and ambiguously gay life partner), director Clint Eastwood went heavy on the face putty and created a couple of bobble-headed characters that look like they belong in a JibJab cartoon, not an Oscar hopeful.

It’s a pity, because the story is compelling. Little is known about the personal life of Hoover, that unsung hero of American history who created the F.B.I. His ruthless quest to promote the agency (and his own public image) while eschewing a spouse, children and pretty much any kind of social life is Shakespearean.

As the younger Hoover, DiCaprio’s a wily charmer. Hammer brilliantly bats his eyelashes (and at one point, flies into a thrilling rage) as Hoover’s doe-eyed sidekick. It should come as a surprise to no one that these two are as endowed in the talent department as they are in the aesthetic arena.

Which makes it all the more disappointing when their performance gets squandered by tired movie-making techniques. They step into the elevator as old men, they emerge as young. Flash back, flash forward. Maybe it’s inevitable in a film that spans seven decades, but the back-and-forth gets old.

Naomi Watts, playing Hoover’s secretary, Helen Gandy, was spared the Age-ometer 3000. But like Hammer and DiCaprio, her best moments happen when she’s playing the younger version of her character. As Hoover’s strong-armed mom, Judi Dench inherits the Best Most Overbearing Mother of the Year award from “Black Swan’s” Barbara Hershey.

Like the limp green beans next to an overdone rib-eye, “J. Edgar’s” over-the-top accents make sense with the caked on makeup. The stand in for Robert Kennedy sounds like Bugs Bunny. Richard Nixon is similarly laughable.

Eastwood’s intentions were good. On execution, less would’ve been more.