I saw the movie yesterday, and "OH MY GOD" what a movie...
The whole movie is shot using a handy cam. Actually your synopsis is not very acurate. The movie starts with a bunch of friends organising a surprise farewell party to the main character (Rob), and filming this party with Rob's camera (so he can take the souvenirs with him)... Only they're filming over an exisiting tape recording (interesting how the director juggles between the 2 recordings) and something huge hits NYC (IMO it's goes way further then a simple Godzilla like monster attack). This huge thing is caught on tape!
The fact that the movie is shot with a handycam makes you feel you're part of it, and more importantly, makes you think what's going on is actually real. The movie is simply breathtaking and the whole Viral Marketing campaign that preceded it was awsome IMO.
JJ Abrams is the producer, something important to note, given JJ's style and love of signs, hidden stuff and teasers. A must see!!!!
And one piece of advice, stay till the very end of the credits and just listen carefully