Cloverfield in hindsight

Now that Cloverfield has debuted there are some questions or comments that have come to light. We will now attempt to pull back the lid on the Cloverfield phenom
How can the head of the Statue of Liberty go bouncing down the street after its been sheared off by a monster? Well, the head itself is about 17 feet tall so yes, it could easily roll down a street like a bowling ball.
It's not believable that the Army commander would give Rob the time of day much less listen to him whine about his girlfriend being stuck inside a building. It's a small point not worth nit-picking over. We're talking about a monster running amuck here.
How would the camera work on batteries for an entire day? Hud doesn't video everything - just about an hour's worth of footage, so yes that would fit on one videotape and the battery would last if it was freshly charged. Besides how do we know that Hud didn't snag an extra battery when he was with Rob looking for a cell phone battery in the electronics store?
What is that killer music playing over the end credits? Michael Giancchino composed a kind of orchestral mash-up of the original Godzilla soundtrack, called "Roar" that plays during the close.
Somebody said in the last scene of the movie you can see something falling into the ocean off Coney Island? Great now I have to go back and see that to see what the hell they're talking about. Of course considering Cloverfield was made by the company that makes Lost it's likely to anticipate some hidden clues.