When I first saw this film, I knew that it was given pretty bad reviews--currently 16% on Rotten Tomatoes and 35% on Metacritic. And with my expectations set that low, I remember kinda liking this movie: sure, the protagonist was unlikeable (as some critics notes)--but that gives him some room to grow as a person; sure, the teleportation power these "Jumpers" have opens up the movie to some action scenes that are hard to follow--but some of the visuals are really interesting; and sure, the villainous group is this pretty incoherent group of religiously-motivated Paladins--but...
That's probably the biggest structural problem with the movie. (As opposed to other sorts of problems, like casting. Hayden Christiansen does good work as the selfish guy who doesn't care about the world, the guy who creeps around the girl he likes after years of not seeing her. But when he starts to act nice, it doesn't really ring true.) Actually, let's expand the issue: I'm fine with the hero's journey from entitled little shit running away from family trauma (mother abandoned, father is cold) to guy willing to put himself out to save others (even if the only time he really does that is to save the girl he likes; and to hold back from killing the antagonist that he never tried to kill before); but the minor/secondary characters need polishing.
First, the antagonists: If you have a character who is self-centered and wants to run away from his past, it makes some thematic sense to make the antagonists interested in tying him down to the world. Unfortunately, the Paladins' religious motivation for this is so hokey that it never really seems like anything but a plot convenience. How about this: you have a character who is both running away from his past and locked into an adolescent, screw-the-world mentality, a guy who won't lift a finger to help people caught in natural disasters. So make his opponents people who know about his past and want to make the world better--by any means necessary: a covert military/intelligence unit. So now we have a self-centered teleporter facing an opponent who seems to have a good idea: use your powers to help people. Of course the leader of the unit will turn out to be power-mad because we don't want too much ambiguity. But now we're left with a hero who has seen what his power can do to help people, and not just see how his power can help him get laid.
Which brings us to similar problems with the other secondary characters: the love interest who mostly just gets pushed around or used as a lure; the vengeance-mad jumper who should really be in more conflict between his jumper and his normal lives; the silly mystery of why his mom left, etc.
But, to end on a good note, there's at least one thing that this screenplay does nicely. When the jumper protagonist returns home and runs into the old bully from high school, he teleports him away as a way to punish the bully. Only that strange event calls up the attention of the bad guys. In that way, the protagonist is punished for his short-sighted and self-centered interest in revenge.