I bought this movie from Criterion thinking a film accepted by them couldn't lead me astray (only later did I learn Armgageddon and The Rock were part of their collection), and boy was I wrong.
This is really one of the most pointless films I've ever seen. It took a big risk trying with it's innovative non linear structure (ala Rashamon) and gambles like this are usually hit or miss; Rashamon was a hit, this was a miss.
The plot is quite similar to Rashamon in that it's told by four separate accounts of the same event, a murder of a prostitute by a soldier, a pimp and wife, a devious night club worker, and a punk kid who were all near the scene and interrogated as suspects. One of the chief problems though is it is missing characters who actually care or discuss what happened, making it hard for a viewer to relate to what he just saw.
In Rashamon the character's discussion at the beginning and end of the trial as it be validated the themes of that movie, not to mention the hollowed out building they sat in to avoid the rain was the chief visual metaphor of the film. There were constant cuts back to that structure throughout the length of the film.
The Grim Reaper really doesn't have that basis so the cinematography and editing just wander around aimlessly, and I use the word wander because the camera is quite free moving about in this film, apparently thats supposed to be one of the virtues of this film.
Overall the central problem of this film is that it's non linear structure and subjective accounts of the same event generally just don't work unless there are common themes and setting throughout or any way for the audience to relate to what just happened. Normally if a film tells a good linear story with beginning to end plot it doesn't have to be particularly meaningful; this film put itself at risk by trying to be innovative and suffered the consequence.