I saw the anime version of Death Note (it's not a movie but a TV series), which has a pretty dazzling animation and complex story, compared to which the few clips of the live-action version seemed sub-par. Thus, although I read positive reviews of the latter, I was disinclined to check it out. As for the anime version, although overall I rate it quite highly, by the end I had three major problems with it:

1. Although the morality of executing murder convicts features prominently, the authors completely omitted the question of judicial error (as if none of the thousands executed by the anti-hero were falsely charged and convicted).
   
2. [SPOILER] It's bold to kill off the hero, but I found the substitute hero less interesting. (Kind of unavoidable when you manage to create such a captivating hero.)
   
3. There was a streak of misogyny throughout, especially the detective woman who was in effect punished by the authors for being a career woman, and the pop star female main character who was so brainless it hurt. (This misogyny also re-surfaced early in the authors' next work, Bakuman.)

As for Battle Royale, I fear my reaction would be similar as in the case of Outrage: the gore wouldn't appeal to me and would take away from the social critique.

_{*Lunatic*, n.
One whose delusions are out of fashion.}