There are three key failings in this script:
1) No Ryuk. Ryuk is easily the single most entertaining aspect of Death Note. He operates in much the same way that the Greek chorus does in classic plays...he in the character that asks the same questions and makes the same observations the audience does. He's the foil for Light to have a reason to explain his plans. Additionally, he also provides much-needed humor to lighten up what is otherwise a pretty darned grim affair of mass-murder. Speaking of which...
2) The reduction of scale. The cool hook of the Death Note concept is that a single person is holding the entire planet hostage; this script ignores this entirely and has Light focus on an extraordinarily limited pool of victims. There's no international intrigue whatsoever, and the mind-games between Kira and L are greatly reduced in importance because there's so much less on the line.
3) Light's entire character is nothing like the original. He's been re-written to be seen as a sympathetic avenger, rather than the sociopathic egomaniac that he was in the original story. The audience is SUPPOSED to find him reprehensible. The script completely shifts the blame to the Death Note itself, ultimately absolving him of some of the guilt. Their goals are completely different: Luke wants revenge for his mother, and Light wants to be God of the world. The original motivation is infinitely more interesting and provides many more challenges.
The problem with this script is that it's not written with sequels in mind, which any Death Note flick will honestly have to do...there need to be at least two movies to tell this story.