Samuel L. Jackson must really have it in for people with super-powers. In M. Night Shyamalan’s “Unbreakable” (2000), he played the dark nemesis to Bruce Willis’ invulnerable would-be hero. And now in Doug Liman’s “Jumper” he’s the implacable head of the Paladins, a centuries-old organization devoted to tracking down, and disposing of, those rare humans who possess—and make use of—the power of teleportation, whom they see as genetic abominations and threats to social order.

Loosely based on a 2002 sci-fi novel by Steven Gould (who recently published another book to explain some of the script’s additions and alterations), the picture tells the story of David Rice (played in the initial reel by Max Thieriot), a shy Michigan high school student who discovers that he can “jump” to another location after accidentally falling through the ice of a frozen river and being presumed drowned. Taking advantage of the ability, he leaves his abusive father (Michael Rooker) and moves to the big city, where the power to teleport into bank vaults and make off with lots of cash enables him to live the high life, jetting without need of plane to the furthest reaches of the globe while based in a lush apartment. Ten years later, Thieriot’s grown into Hayden Christensen—a pretty good physical match, actually, though the younger version is actually more animated and personable than the rather dour, poker-faced older one played by the erstwhile Anakin Skywalker.

But despite all his wealth and travel options, David’s left clues that allow the malevolent Roland (Jackson) to track him down, and after barely escaping his pursuer he makes the further mistake of returning home to see Millie (Rachel Bilson), the girl he loved from afar in high school and is still pining over. By doing so he puts Roland on his trail again, and by persuading her to go to Rome with him (by regular means of transport), he makes her a pawn Roland can use against him. Simultaneously he attracts the attention of another jumper, Griffin (Jamie Bell), who’s out to destroy all the Paladins but resists David’s suggestion that they join forces. But of course they inevitably do.

What follows is an elaborate but messy sci-fi chase filled with fights and narrow escapes but marked by flat characterization, a narrative rife with illogic, and surprisingly poor special effects, which consist mostly of people and things abruptly skipping ahead in a frame to indicate the result of teleportation. (The effect is jerky and kind of sloppy.) Liman is obviously aware of the deficiencies, and tries to cover them with a manic energy that works much less successfully here than it did in “The Bourne Identity.” He’s not helped by the blankly boyish quality of Christensen, which seemed just right for his role in “Shattered Glass” (easily his best performance) but was dull in the “Star Wars” movies and is even more so here. (It might have been a better choice to concentrate on Thieriot’s younger version of the character.) Bell, who in the past has exhibited a hangdog charm in pictures as varied as “Billy Elliot” and “The Chumscrubber,” is frantic and unlikable here, and Bilson is so pouty she makes one wonder what David could possibly see in the grown-up Millie (AnnaSophia Robb) is considerably better as the younger version). Rooker is, as usual, suitably nasty as David’s abusive dad, but it’s difficult to make sense of Diane Ladd’s role as the boy’s mother, who abandoned the family years before but shows up as a Paladin. (There’s no plausible explanation for how such a woman could ever have been married to Rooker.)

As for Jackson, he snarls his way through his villainous turn, letting his bleached-white hair stand in for acting. It’s an embarrassing turn that could be made worse only if a threatened sequel doubled up this movie with one of his previous disasters. Just think of “Jumpers on a Plane.”

But there’s little chance of that, or any other follow-up to “Jumpers,” one of those sad instances of a potentially intriguing premise being completely botched in the execution.