For fiction writers the choice of point of view (POV) is always a sticky one. The POV you choose affects the way the story is told. You can't tell the same story in first person that you could tell in third or omniscient. It has been interesting to watch the evolution of POV in film. It is as if screenwriters have suddenly awakened and discovered that yes there are other POVs besides third person. Its like a lightbulb slowly turned on after the release of the Blair Witch Project.
One of the things that really worked for me in Cloverfield was the immediacy and personalization lent by the first person viewpoint of the filming. Perhaps it is because I lived through 9/11 in NY and I know how confusing it is to be in the middle of an epic disaster. There are certainly scenes in the movie that borrowed directly from real-life, at least from my perspective. When you are stuck in the middle of a disaster you have only rumor, speculation and your own eyes to rely on.
With a first person narrator the viewer has to do more work. Their mind and emotions are engaged in the process, which can make for much more extreme reactions to a movie. First person also requires an additional level of suspension of disbelief. The viewer has to work on in their own heads the reasons for certain things -- such as the extremely rapid response of the military. Perhaps the monster was expected? Maybe the US government knew it was coming, but didn't know where and when it would show up. These are things that a typical monster movie or disaster movie such as Independence Day would show you. The drama is less personal and focused because the POV is wider.
There is only one part of the movie that didn't work for me. They gave away the monster too soon. When you are working with first person, an unreliable narrator if ever there was one, the tension build up is immense and it takes a good feel for audience and plotting to find the exact moment to release the tension. Since this is one of the first few movies to deal in this POV I can see why the director and/or screenwriter released the tension too soon -- I'm sure it was fear that the audience wouldn't react well if there wasn't a big pay-off right away. In my mind I would have cut some of the beginning sequence before the monster in order to build the tension more after it shows up.
Overall it was a faboo movie and, with the way it ended, I can certainly see the possibility of a sequel. Hopefully when they do make it, the filmmakers will take the lessons learned from the first movie and use first person POV to its best advantage.